Chama broke the deadlock on nine minutes with a powerful shot halfway. The lead will only last for two minutes before Bilel Ajmi drew level.
Ajmi shot the Tunisians into the lead for the first time few minutes later before Chama pulled even from a free-kick at the edge of the penalty area that Tunisian defender Moez Trabelsi failed to stop.
Just before the break, Ajmi saw the first red card of the tournament, fouling his marker after he was dispossessed of the ball after a failed attempt to dribble his way through.
The Tunisians resumed a man-less but the Zambians failed to make the most of their numerical advantage in the opening minutes.
On 32 minutes, Chama completed his hat-trick with an acute angled shot before Kelvin Kangwa took the game beyond the North Africans minutes later.
Zambia share top spot with Mozambique on three points apiece, after the latter thumped host South Africa 7-4 in the opening game of the tournament.
The Zambians will next face South Africa on Sunday whilst Mozambique squares Tunisia.