According to the BATF you can own a "Short-Barreled Shotgun". You must either:
(1) By transfer after approval by ATF of a registered weapon from its lawful owner residing in the same State as the transferee.
(2) By obtaining prior approval from ATF to make NFA firearms.
[27 CFR 479.62-66 and 479.84-86 ]
A $200 tax stamp must be paid to the BATF NFA division.
All info from the BATF website.
Aggie80