According to Illinois State Law, You CANNOT buy Alcohol a day before you turn 21... as stated in the official law:

"It is unlawful to sell, serve, deliver or give alcoholic beverages to a person under 21 years of age or to any intoxicated person. Violation of this provision is a Class A Misdemeanor."

(Source : www.state.il.us/lcc/alcohol.htm)

In certain OTHER states you can legally buy alcohol the day before you turn 21.

For Example,

According to the Virginia ABC website, "The Attorney General's Office has opined that a person attains his/her next year of age on the day prior to his/her birthday."

This means you may purchase alcohol the day prior to your 21st birthday in VA. SO check your states local law for specific age requirements when dealing with alcohol.