We report the first observation of linear magnetoresistance (LMR) in multilayer epitaxial graphene grown on SiC. We show that multilayer epitaxial graphene exhibits large LMR from 2.2 K up to room temperature and that it can be best explained by a purely quantum mechanical model. We attribute the observation of LMR to inhomogeneities in the epitaxially grown graphene film. The large magnitude of the LMR suggests potential for novel applications in areas such as high-density data storage and magnetic sensors and actuators.