Hi Allen, no sir, this is banned by name in Illinois.
Prohibited - All Thompson rifles, including the following:
I. Thompson M1SB.
II. Thompson T1100D.
III. Thompson T150D.
IV. Thompson T1B.
V. Thompson T1B100D
VI. Thompson T1B50D.
VII. Thompson T1BSB.
VIII. Thompson T1–C.
IX. Thompson T1D.
X. Thompson T1SB.
XI. Thompson T5.
XII. Thompson T5100D.
XIII. Thompson TM1.
XIV. Thompson TM1C
budsgunshop.com/feeds/state_reg/illinois_restrictions.pdf

Hi Allen and welcome. Unfortunately, no Sir. This is considered an Assault Rifle by IL gun law standards although it really is just a pistol caliber carbine. Shame, but stay safe!