If you're uncomfortable going completely naked or you are afraid of even the remote possibility of legal scuffles, then don't go completely naked.
You don't need to cover up much to be legal. The local laws on nudity in practice are a balance between public complaints and officer discretion.
Either wear something skimpy that you're comfortable in, or simple use the incredible transforming powers of a little body paint, a sock, or tape.
For some ideas see past year's photos
As mentioned in the ride guidelines, for maximum First Amendment protection integrate nudity with your message: "burns fat not oil", "nude not lewd", "no concealed weapons", "naked is how vulnerable I am sharing the roads with cars"
Technically Chicago code allows a FINE
for exposed genitals, pubes, anal areas, and women's nipples. Getting arrested requires adding some mix of alcohol, non-compliance, no ID, belligerence, etc. Not a substitute for real legal advice, full city code below:
8-8-080 Indecent exposure or dress.
Any person who shall appear, bathe, sunbathe, walk or be in any public park, playground, beach or the waters adjacent thereto, or any school facility and the area adjacent thereto, or any municipal building and the areas adjacent thereto, or any public way within the City of Chicago in such a manner that the genitals, vulva, pubis, pubic hair, buttocks, perineum, anus, anal region, or pubic hair region of any person, or any portion of the breast at or below the upper edge of the areola thereof of any female person, is exposed to public view or is not covered by an opaque covering, shall be fined not less than $100.00 nor more than $500.00 for each offense. (Prior code § 192-8; Amend Coun. J. 12-4-02, p. 99931, § 5.4)
Also note bike headlight
law: Chicago Muni Code 9-52-080(a):
Every bicycle when in use at nighttime shall be equipped with a head lamp which shall emit a white light visible from a minimum distance of 500 feet from the front and with a rear red reflector capable of reflecting the head lamp beams of an approaching motor vehicle back to the operator of such vehicle at distances up to 200 feet or a rear lamp emitting a red light visible from a distance of at least 200 feet from the rear.
Also see this important CAPS bulletin
to bike massers.