Chirality is one of the most prominent and intriguing aspects of nature, from spiral galaxies down to aminoacids. Despite the wide range of living and non-living, natural and artificial chiral systems at different scales, the origin of chirality-induced phenomena is often puzzling. Here we assess the onset of chiral optomechanics, exploiting the control of the interaction between chiral entities. We perform an experimental and theoretical investigation of the simultaneous optical trapping and rotation of spherulite-like chiral microparticles. Due to their shell structure (Bragg dielectric resonator), the microparticles function as omnidirectional chiral mirrors yielding highly polarization-dependent optomechanical effects. The coupling of linear and angular momentum, mediated by the optical polarization and the microparticles chiral reflectance, allows for fine tuning of chirality-induced optical forces and torques. This offers tools for optomechanics, optical sorting and sensing and optofluidics.