A gas-loaded undulator is proposed as a method for the coupling of intense optical radiation and charged particles to achieve high-gradient acceleration of 100 MeV/m or more. The theory of the gas-loaded inverse free electron laser (IFEL) is the same as that of the vacuum IFEL, with the exceptions that the phase-matching condition between the optical field and the charged particle is changed, and that multiple scattering of the electrons by the gas molecules has been introduced. The new phase matching condition allows reasonable undulator magnetic fields while still maintaining good acceleration gradients for extremely relativistic beams. Synchrotron radiation losses can then be kept to acceptable values. A Monte Carlo simulation of the interaction has been done which includes elastic scattering, radiation losses, laser and electron beam characteristics, and gas and helix parameters. As with the conventional IFEL, tapering the undulator with an increasing magnetic field is found to affect both the maximum energy and population of the accelerated particles.