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I don't think an engine for this would be hard to program. What would be hard is to make it search deep enough to acquire a reasonable skill. The way I would do it, is to use 4 recursive calls to the search routine for each turn, (or as many as you have Chieftains), doing the negamax flip only once every 4 ply. Each ply would cycle through all pieces, for each piece, cycle through all Chieftains, for each Chieftain that is within range, replace that Chieftain by an 'exhausted Chieftain' (a different piece type, that moves as a Chieftain, but has no activation power) and generate all moves with the piece, and play them out one by one. After moving the piece, you recurse. For efficiency you would keep track of the number of 'charged' Chieftains, and if your move just exhausted the last one, you flip the turn (and score, etc.), and 'recharge' the opponent's Chieftains. I would rely on hash hits to weed out the intra-turn transpositions, probing after each ply. (The turn-phase would automatically be hashed, because the charging and exhausting of Chieftains would alter the hash key.)

That is realy all. But now try to reach meaningful depth...