From the Chicken documentation [1] it appears that it does not include bignums in the core but as a separate package that requires GMP [2] to be installed. Since GMP is LGPL licensed this might cause an issue if you are sensitive to such things.
Gambit includes bignum support without external dependencies.
[1] http://wiki.call-cc.org/man/4/Deviations%20from%20the%20stan...
(I use Gambit but not Chicken)