Using a new, parameter-free first principles strategy for modeling sublimation growth, we show that while Al and N2 dominate gas concentrations in AlN sublimation growth chambers under typical growth conditions, N2 is undersaturated with respect to the crystal and therefore cannot be a growth precursor. Instead, our calculations predict that the nitrogen-containing precursors are Al(n)N (n=2,3,4), in stark contrast to assumptions used in all previous modeling studies of this system.