Momentum exchange was observed between laser light and an electron beam using the inverse Čerenkov effect. This interaction was accomplished by introducing a gas with an index of refraction which reduced the phase velocity of the light wave to match the velocity of the electron. A 30-MW Nd: YAG 1.06-μm laser intersected 102-MeV electrons at an angle of 18 mrad in hydrogen gas. The beams overlapped in the interaction region for approximately 105 optical wavelengths. The energy exchange by the inverse Čerenkov effect was verified in two ways: First, a change was observed in the electron energy distribution in the presence of the laser, and second, this change was observed to be a function of the index of refraction, as determined by the pressure of the gas. A +/-13% variation about the pressure for optimum energy exchange reduced the interaction by one-half. The results of the experiment agree with the predictions of a Monte Carlo computer simulation of the interaction. Methane gas was also investigated as a phase-matching medium. Possible applications include laser-driven particle accelerators and stimulated Čerenkov devices, such as optical klystrons and traveling wave tubes.