  Exotic new particles carrying baryon number and with mass of order the
nucleon mass have been proposed for various reasons including baryogenesis,
dark matter, mirror worlds, and the neutron lifetime puzzle. We show that the
existence of neutron stars with mass greater than 0.7 $M_\odot$ places severe
constraints on such particles, requiring them to be heavier than 1.2 GeV or to
have strongly repulsive self-interactions.
