The chemical process that occurs in the mitochondria during ATP production is known as oxidative phosphorylation. This process involves the electron transport chain and chemiosmosis, where electrons are passed through protein complexes, releasing energy that helps pump protons into the intermembrane space. The resulting proton gradient drives ATP synthesis as protons flow back into the mitochondrial matrix through ATP synthase. This efficient energy production is vital for cellular functions, underscoring the mitochondria's role as the powerhouse of the cell.