It depends what you're looking for, but I was very surprised to discover a few months ago that the Dominick's closest to me carries suka, Mama Sita's adobo and kare-kare mix, banana ketchup...and a few other things.
Also, just across the street from that Dominick's is a Butera that I think also carries the aforementioned items plus a few more. I never would have thought there'd be the demand for these things in my neighborhood (in contrast to, say, Niles), but there'll all there, granted with prices slightly higher than you'd find at Filipino markets.
DOMINICK'S
1042 S. Elmhurst Rd
Mt Prospect, IL 60056
Butera
727 W Golf Road-Des Plaines, Il 60016
Tel.847-228-1112 Fax.847-439-6992
Mon-Sat 7am-9pm;Sun 7am-8pm