We report the appearance of chimera states in a minimal extension of the classical Vicsek model for collective motion of self-propelled particle systems. Inspired by earlier works on chimera states in the Kuramoto model, we introduce a phase lag parameter in the particle alignment dynamics. Compared to the oscillatory networks with fixed site positions, the self-propelled particle systems can give rise to distinct forms of chimeras resembling moving flocks through an incoherent surrounding, for which we characterize their parameter domains. More specifically, we detect localized directional one-headed and multi-headed chimera states, as well as scattered directional chimeras without space localization. We discuss canonical generalizations of the elementary Vicsek model and show chimera states for them indicating the universality of this novel behavior. A continuum limit of the particle system is derived that preserves the chimeric behavior.