Moon situation for Shawwal in 2006 at Chicago IL:
Oct 21st, Moon is already set before Sunset at 6:05pm. No chances of sighting.
Oct 22nd, Moon is already set with Sunset at 6:03pm. No chances of sighting.
Moon situation at 6:13pm on Oct 23rd. Fair chances of sighting.
Bukhari Volume 3, Book 31, Number 133: Narrated Abu Huraira: The Prophet or Abu-l-Qasim said, "Start fasting on seeing the crescent (of Ramadan), and give up fasting on seeing the crescent (of Shawwal), and if the sky is overcast (and you cannot see it), complete thirty days of Sha'ban."