The ultrafast excited-state dynamics of 2,4,6-triaminopyrimidine - thought to be a promising candidate for a proto-RNA nucleobase - have been investigated via static multireference quantum-chemical calculations and mixed-quantum-classical/trajectory surface-hopping dynamics with a focus on the lowest-lying electronic states of the singlet manifold and with a view towards understanding the UV(C)/UV(B) photostability of the molecule. Ultrafast internal conversion channels have been identified that connect the lowest-lying ππ* electronically-excited state of 2,4,6-triaminopyrimidine with the ground electronic state, and non-radiative decay has been observed to take place on the picosecond timescale via a ππ* out-of-plane NH2 ("oop-NH2") minimum-energy crossing point. The short excited-state lifetime is competitive with the excited-state lifetimes of the canonical pyrimidine nucleobases, affirming the promise of 2,4,6-triaminopyrimidine as an ancestor. Evidence for energy-dependent excited-state dynamics is presented, and the open question of intersystem crossing is discussed speculatively.