We present transport measurements of a nondegenerate two-dimensional electron system on the surface of liquid helium at a point constriction. The constriction is formed in a microchannel by a split gate beneath the helium surface. The electrostatic energy of the electron system, which depends in part on the electron density, determines the split-gate voltage threshold of current flow through the constriction. Steplike increases in conductance are observed as the confinement strength is reduced. As the Coulomb interaction between electrons is strong, we attribute this effect to the increase in the number of electrons that can pass simultaneously through the constriction. Close to the threshold, single-electron transport is observed.