The strikes affect the hotels on Wacker Drive and at McCormick Place.
The workers are joining union members in three other cities who also walked off their jobs on Thursday.
Members of the Unite Here union have been in negotiations with Hyatt since 2009. One company official says he is "very disappointed."
"Right now we have a great offer on the table, which equals the financial and healthcare benefits packages of both the Sheraton and the Hilton," said Hyatt Regency Chicago General Manager Patrick Donelly.
"We agreed on the benefits and the wages," said employee Francine Jones. "But they can give that to us at anytime. That's been agreed on. There's some other stuff that we need. The housekeeping language has not yet been spoken about."
Donelly says the next round of negotiations are scheduled for September 15. He said guests are not impacted by the strike.