Ambient-pressure-grown LaO0.5F0.5BiS2 with a superconducting transition temperature Tc ∼ 3 K possesses a highly anisotropic normal state. By a series of electrical resistivity measurements with a magnetic field direction varying between the crystalline c-axis and the ab-plane, we present the first datasets displaying the temperature dependence of the out-of-plane upper critical field H ⊥ c2 (T ), the in-plane upper critical field H / / c2 (T ), as well as the angular dependence of Hc2 at fixed temperatures for ambient-pressure-grown LaO0.5F0.5BiS2 single crystals. The anisotropy of the superconductivity, H / / c2 /H ⊥ c2 , reaches ∼16 on approaching 0 K, but it decreases significantly near Tc. A pronounced upward curvature of H / / c2 (T ) is observed near Tc, which we analyze using a two-gap model. Moreover, H / / c2 (0) is found to exceed the Pauli paramagnetic limit, which can be understood by considering the strong spin-orbit coupling associated with Bi as well as the breaking of the local inversion symmetry at the electronically active BiS2 bilayers. Hence, LaO0.5F0.5BiS2 with a centrosymmetric lattice structure is a unique platform to explore the physics associated with local parity violation in the bulk crystal.