It depends on what you mean. While a marine is on active duty, he can carry a gun if the duty requirements allow it. If you mean can a marine carry a gun when not on duty simply because he is a member of the armed forces, no. Military personel must follow the law of whatever state they are in when they are not on base and off duty.
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Not if you are a sovereign Marine (Note: Not Sovereign citizen). A sovereign Marine is a Marine contracted with the U.S. being a Marine integrated with the U.S. but not absolutely under the U.S. Jurisdiction.