Which great lake is closest to Michigan?

Ahh -- my home state. It's motto is "If you seek a beautiful peninsula, look around you.

It's bordered by four Great Lakes -- Lake Superior, Lake Michigan, Lake Huron, and Lake Erie.

which one is close to chicago?

Chicago is in Illinois, not Michigan.

Chicago is on the southern shore of Lake Michigan.

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is there a bay or harbor that is in Chicago that goes into lake Michigan?

No, it's not on a bay. Chicago is spread out along the shores of Lake Michigan, and has 10 harbors.

http://www.chicagoharbors.info/

To find out which Great Lake is closest to Michigan, you can refer to a map or use an online mapping service. Michigan is surrounded by four of the five Great Lakes: Lake Superior, Lake Michigan, Lake Huron, and Lake Erie. The closest Great Lake to Michigan is Lake Huron. It is located to the east of Michigan and is connected to it by the Straits of Mackinac.