Please go through:
Mac OS X Mavericks (10.9) compatibility FAQs | CC, CS6, Acrobat
You can also follow the forum threads & check if it resolves the issue:
Re: After upgrading to Maverick OS X, Illustrator CC will not open
Re: Illustrator CS6 and CC repeatedly crashing since I installed Mavericks (no plugins installed)
Please let us know if it worked.
Regards
Rajshree