Nivinivinack is a technique for determining priority in game play. One player holds both fists forward, with a small pyramid (or other token) hidden in one of them. The other picks one of the fists, winning if it is the one that contains the pyramid.
A form of nivinivinack is traditional for determining color (and thus priority) in standard chess, where a white pawn is held in one fist and a black in the other. But in Martian Chess (or Monochrome Chess) it must be a full fist and an empty one. Pyramid pawns are small enough that the difference between full and empty fists should not be visually obvious except in the tiniest hands.
The term nivinivinack dates back to at least 1653, when it figures in Thomas Urquhart's translation of Rabelais' Gargantua.