Quitting Prior to Completion of Initial Term

My question involves labor and employment law for the state of: IL

I am looking to resign prior to completing initial term of contract, but will give full 60 day notice required.

Contract "The initial term of the Agreement shall be for one year beginning on August 15, 2013 and shall be deemed to be extended automatically therafter upon the same terms and conditions, until either party shall give written notice to the other of its intention to terminate employment on a date no sooner than 60 days after the date of notice, in which case employment shall terminate as of the date indicated."

When is the soonest I can get out of this contract?

You can quit any time you want. Whether the employer might have recourse will depend on the nature of your work and the other provisions of the contract.