We calculate the properties of static strange stars using a quark model with chiral mass scaling. The results are characterized by a large maximum mass (～1.6 M⊙) and radius (～10 km). Together with a broad collection of modern neutron star models, we discuss some recent astrophysical observational data that could shed new light on the possible presence of strange quark matter in compact stars. We conclude that none of the present astrophysical observations can prove or confute the existence of strange stars.