Could parts of Chicago be considered an island?

Looking at a map recently, I noticed that much of Chicago, from about the Loop down to about Blue Island in the south suburbs, is completely surrounded by water (Lake Michigan, a river or two, and some man made canals). And since some of these aforementioned rivers empty into the Mississippi, I realized that it would be impossible to travel from the east coast to the west coast without crossing a body of water. So would I be technically correct in saying that Chicago (or parts of it) is an island?

Yes.

But although I lived there 15 years, and still work on the Loop island, I’ve never heard it referred to in those terms. Still, there’s a big patch of land that you can’t get off of without crossing water.

Canals tend not to count when it comes to defining large islands. For instance, nobody thinks of Spain and Portugal as forming an island, even though the Canal du Midi means that it’s possible to sail across sourthern France from the Atlantic coast to the Mediterranean. It’s still the Iberian Peninsula. I suspect most people would regard the Chicago case as similar.
Incidentally, on the separate question of having to cross water at some point in travelling from the east to west coast within the US, then you don’t even have to appeal to canals. Several pretty sizable tributaries of the Missouri flow into Montana from Canada.

There is Goose Island in the Chicago River (crossed by Division Street between Elston and Halsted). However, it was created artificially by digging the North Branch Canal which is now on its east side. See http://www.consciouschoice.com/biking/biking1509.html