This may actually be a sign that he is getting more mature, not less. He is still only 3, and disappointment is awfully hard to take at that age, particularly when it blindsides you. He may be starting to actually set up series of combination moves and plans of attack several moves in advance, and when he loses a piece that was integral to his plans, suddenly he is faced not only with the prospect of potentially losing the game (which may or may not really bother him), but with the sudden and irrevocable loss of the beautiful thing that he was building. Just finding out that it was flawed and not the marvelous and elegant strategy that he thought it was could really feel heartbreaking.
Having him play variations, playing against a computer with an "undo" function, and having him show and tell you what he had had planned might help. Asking him if he is sad, or angry, or disappointed and letting him know that you understand how he feels when his plans don't work out might help stop or prevent the "freak-out". Sometimes kids just don't have access to the words to communicate their feelings once they get upset at this age (even if they have them when they aren't upset), and having a parent provide the scaffolding to help them communicate can be really helpful. I would agree that a full-blown tantrum would be the signal to stop the game for a little while so that he can regain some calm and self-control. I'd make sure that you recognize and praise his self-control and good sportsmanship when he loses a piece (even a pawn) and holds it even somewhat together.
