James Gandolfini -- Theft Victim in Death ... Rolex Submariner M.I.A.

James Gandolfini suffered an indignity after he died in Rome -- someone apparently stole his expensive Rolex watch within hours after he died ... TMZ has learned.

We've obtained an insurance form filed by James' people. According to the form and family sources, someone stole a $3,000 Rolex submariner watch from James' hotel room on the day he died.

The insurance form says there was no damage to the room and there's no mention of forced entry. There's no suspect listed on the form ... but the implication is that someone may have pilfered the item during the commotion following the heart attack that killed the actor.

The form doesn't specifically describe the type of submariner that was stolen, but they vary wildly -- some are diamond encrusted, some are platinum and some are gold.