A multicomponent anti-Widom-Rowlinson lattice gas is introduced. An arbitrary numberM of particle types is permitted, all having the same activity. The only interactions are nearest-neighbor exclusions oflike particles (analogous to map-coloring problems). For any lattice it is shown that there is a finite numberM 0 (depending only on the coordination number of the lattice) such that for allMM 0 the infinite volume correlation functions exist and are analytic functions of the activity, for all positive values of the common activity.