First, as your description makes clear, you are not on J-1, you are on H-1B.
There is nothing in either the statute or the regulations governing H-1Bs that would prohibit a non-compete clause in a contract.
J Charles Ferrari Eng & Nishimura 213.622.2255 The statement above is general in nature, as not all the facts are known. You should retain an attorney to review all the facts specific to your case in order to receive advise specific to your case. The statement above does not create an attorney/client relationship.