BSA on charter partners:
http://www.scouting.org/factsheets/02-507.html
...
  Schools, community and religious organizations, with the help of the
  BSA, organize Cub Scout packs, Boy Scout troops, Varsity Scout teams,
  Venturer crews, and Learning for Life groups for children and youth.
  They manage these units and control the program of activities to support
  the goals and objectives of the chartered organizations. 
...

Units are owned & operated by the chartering organization, NOT the Boy Scouts:
...
  To support approximately 124,000 Scouting units owned and operated by
  chartered organizations,
...

Earlier successful ACLU lawsuit against Chicago chartering BSA units:
http://www.aclu-il.org/press/scouts410.html
The successful settlement:
http://archive.aclu.org/news/n020498a.html
Suit against all gov't charters
http://www.aclu-il.org/press/SCOUTfl.html
The lawsuit as filed
(contains explanation of how government charters violate the law):
http://www.purespeed.com/mg/bsa_IL_District.html
The above suit later had to be changed, since the ACLU wasn't able to
get class-action status; it is now two suits, one against HUD grants
and one against the DoD.

Federal BSA charters

I've listed the troop, location, web page URL
and a quote from the URL that specifies the charter/sponsor
There are a lot more that are ambiguous (e.g. they meet at an
AFB but don't list a sponsor); these all state a charter/sponsor.
Remember, they could be out of date.

Troop 232, Sheppard Air Force Base, Texas
http://samgraham.org/Troop232/troop232.htm
Troop 232 is sponsored by the 82d Communications Squadron

Troop 38, 12 FTW (12th Flying Training Wing) Randolph AFB, Texas
http://www.geocities.com/Yosemite/Trails/7438/
We are Chartered by the 12 FTW Randolph AFB

Troop 411, Moody AFB, Georgia
http://www.datasys.net/~dbaisch/troop411/history.htm
1997: Charter granted to 347th Composite Wing, Moody AFB (latest listed)

Troop 392, Patrick AFB, Florida
https://www.patrick.af.mil/45SW/PA/INTERNAL/MISSILER/2001/Feb01/16Feb/patrick_scout.htm
Cox's Eagle rank was presented recently during a ceremony at the
Patrick AFB chapel for Troop 392 which the Chapel sponsors.

Troop 220, Robins AFB, Georgia
http://www.geocities.com/bsa_troop220_rafb/
We are proudly sponsored by the 116th Air Control Wing/Operations Group
(JSTARS), Robins AFB Georgia.

Troop 342, Shaw AFB, Sumpter, South Carolina
http://www.bsa.net/sc/t342/
Current Chartering Organization: 20th Communications Squadron, USAF

http://www.bsa.net/sc/p337/
Shaw AFB Original Charter: 5 October 1998
Chartering Organization: 20 Communications Squadron, USAF

Pack 296, Dyess AFB, Texas
http://www.chisholm-trail-bsa.org/council/scouting_units.htm
7th BW/HC

Troop 296, Dyess AFB, Texas
http://www.chisholm-trail-bsa.org/council/scouting_units.htm
7th Security Forces Squadron

Pack 162, Wright-Patterson AFB, Ohio
http://www.pack162.org/about.htm
Pack 162 is sponsored by Wright Patterson Air Force Base

Troop 91, Travix AFB, California
http://troops.scouter.com/ak/troop8091/
chartered by the 60th Component Repair Squadron

Troop 509, Hurlburt Field AFB, Flordia
http://troop509.org/whoarewemap.htm
we are sponsored by Hurlburt Field

Pack 320, Kent, Washington
http://www.geocities.com/Yosemite/Rapids/7996/news_feb98.html
The 3rd battallion of the 161st Infantry is our Chartered Organization

Troop 173, Carlisle barracks
http://www.carlisle.army.mil/todaycb/scouts/boy_s.htm
Boy Scout Troop 173, in the Kittatinny District of Keystone Council
is chartered by the U.S. Army War College, Carlisle Barracks P.A. 

Troop 1567, Subase Bangor, Washington
http://members.doubleknot.com/Pack4567/about/ScoutingOnSubase/scoutingonsubase.html
Sponsored by the PACNORWEST MWR
(Naval Surface Group Pacific Northwest dept. of Morale, Welfare, & Recreation)
This is part of the same BSA district that kicked out Darrell Lambert
for being an atheist a few months ago.

A *lot* of overseas units are chartered by the military;
these are just from one council, the Far East Council:

Pack 22 & Troop 22, NAF (Naval Air Facility) Atsugi, Japan
Pack 38, CFAY (Commander Fleet Activities Yokosuka) Negishi, Japan
Pack 18, NAF Misawa, Japan
Pack 76 & Troop 76, Comfleact (Commander, Fleet Activities) Sasebo, Japan
Troop 14, 35th Logistics Group, Japan
Pack 33, US Navy Ship Repair Facility, Yokosuka, Japan
Troop 35, US Naval Hospital, Yokosuka, Japan
Troop 45, 374th Supply Squadron, Yokota, Japan
Troop 21, CHPPNPAC, Zama, Japan
Troop 34, AUSA, Zama, Japan
All of the above info from
http://www.scouts.gol.com/page31.html

Okinawa, Taiwan, & Thailand
Units chartered by Camp Foster Chapel
Pack 101, 112 & Troop 101
Units chartered by Kadena Chapel, Kadena Air Base
Pack 102 & Troop 102 (http://www.geocities.com/kabtroop102/)
Units chartered by Camp Kinser Chapel
Pack 103 & Troop 103
Units chartered by 18th Security Forces Sq.
Pack 104, 115 & Troop 109
Units chartered by Camp Courtney Chapel
Pack 110 & Troop 110
http://www.opug.org/bscouts/OkiUnit.html

Pack 80, Hannam Village Chapel, Yongsan, Korea
Pack 81, 20th Area Support Group, Taegue, Korea
Pack 86, Osan Air Base Chapel, Korea
Troop 79, Hannam Village Chapel, Yongsan, Korea
Troop 80, 18th Medical Command , Korea
Troop 81, 20th Area Support Group, Taegue, Korea
http://www.scouts.gol.com/page25.html

http://www.torii.army.mil/archives/archives/2002/mar/15/CGCorner/
.....charted with the 17th ASG such as Boy Scout Troop #21 and 31,..

US embassies charter scout units:
Troop 980, Ukraine, Kyiv, chartered by the US embassy
This posting mentions a troop chartered by us embassy
http://listserv.tcu.edu/listserv/cgi-bin/wa.exe?A2=ind0206&L=scouts-l&D=1&O=D&P=53466

This is part of the BSA's "Direct Service" program:
http://www.directservicebsa.org

I'm sure there are more embassies doing this, but it's hard to find.
I contacted the state department, but they were no help.

There are interesting regulations for BSA units and private
organizations on military bases (FECBSA is the Far East Council,
Boy Scouts of America):

http://www.cnfj.navy.mil/Admin/instructions/5000%20SERIES.htm
http://www.cnfj.navy.mil/Admin/instructions/5720.11F%20Instruction.doc
..."4.5.4.   The FECBSA and USAGSO-WP will not:

4.5.4.1.   Permit unlawful discrimination in their membership based on
race, color, religion, or national origin. "

http://www.langley.af.mil/wm_source/1_fw_source/staff_agency/JA/afi34-223.pdf
...
2. Types of POs. This instruction applies to all POs with the exception
of the following organizations that are governed by DoD Directives (DoDDs)
and Instructions (DoDIs) as referenced:
2.1. Scouting organizations operating at US military installations
located overseas (DoD Instruction 1015.9, (e), Professional United
States Scouting Organization Operations at United States Military
Installations Located Overseas).
[notice only covers overseas, domestic is covered by this]
...
10.2. POs may not discriminate in hiring practices or membership
policies based on the basis of age, race, religion, color, national
origin, ethnic group or gender.
...

http://www.dtic.mil/whs/directives/corres/html/100015.htm
...
6.12.  No person because of race, color, creed, sex,
age, disability or national origin, shall be unlawfully
denied membership, unlawfully excluded from participation,
or otherwise subjected to unlawful discrimination by
any private organization on a DoD installation covered
by this Instruction.   DoD installations will publicly
disseminate information on procedures for individuals
to follow at the local installation when unlawful discrimination
by private organizations is suspected.
...
overseas:
http://www.dtic.mil/whs/directives/corres/html/10159.htm