Green’s Dictionary of Slang

1. (W.I.) short and stout; thus chuck-up man, a short, stout person.

1943

cited in Cassidy & LePage Dict. Jam. Eng. (1980).

2. crowded, full.

1986

O. Senior ‘Real Old Time T’ing’ Summer Lightning 62: You no mus want get rid of some of this junk. They make the place so chuck-up there is hardly anywhere to walk.