  We study a superconducting quantum point contact made of a narrow In$_{0.75}%
$Ga$_{0.25}$As channel with Nb proximity electrodes. The narrow channel is
formed in a gate-fitted constriction of InGaAs/InAlAs/InP heterostructure
hosting a two-dimensional electron gas. When the channel opening is varied with
the gate, the Josephson critical current exhibits a discretized variation that
arises from the quantization of the transverse momentum in the channel. The
quantization of Josephson critical current persists down to the single-channel
regime, providing an unambiguous demonstration of a
semiconductor--superconductor hybrid Josephson junction involving only a single
ballistic channel.
