New mapping reveals 100 probable impact craters on Triton wider than 5 km diameter. All of the probable craters are within 90° of the apex of Triton's orbital motion (i.e., all are on the leading hemisphere) and have a cosine density distribution with respect to the apex. This spatial distribution is difficult to reconcile with a heliocentric (Sun-orbiting) source of impactors, be it ecliptic comets, the Kuiper Belt, the scattered disk, or tidally-disrupted temporary satellites in the style of Shoemaker-Levy 9, but it is consistent with head-on collisions, as would be produced if a prograde population of planetocentric (Neptune-orbiting) debris were swept up by retrograde Triton. Plausible sources include ejecta from impact on or disruption of inner/outer moons of Neptune. If Triton's small craters are mostly of planetocentric origin, Triton offers no evidence for or against the existence of small comets in the Kuiper Belt, and New Horizons observations of Pluto must fill this role. The possibility that the distribution of impact craters is an artifact caused by difficulty in identifying impact craters on the cantaloupe terrain is considered and rejected. The possibility that capricious resurfacing has mimicked the effect of head-on collisions is considered and shown to be unlikely given current geologic constraints, and is no more probable than planetocentrogenesis. The estimated cratering rate on Triton by ecliptic comets is used to put an upper limit of ∼50 Myr on the age of the more heavily cratered terrains, and of ∼6 Myr for the Neptune-facing cantaloupe terrain. If the vast majority of cratering is by planetocentric debris, as we propose, then the surface everywhere is probably less than 10 Myr old. Although the uncertainty in these cratering ages is at least a factor ten, it seems likely that Triton's is among the youngest surfaces in the Solar System, a candidate ocean moon, and an important target for future exploration.