Sub-Kelvin scanning tunneling spectroscopy in the Chevrel phases SnMo6S8 and PbMo6S8 reveals two distinct superconducting gaps with Δ1=3  meV, Δ2∼1.0  meV and Δ1=3.1  meV, Δ2∼1.4  meV, respectively. The gap distribution is strongly anisotropic, with Δ2 predominantly seen when scanning across unit-cell steps on the (001) sample surface. The spectra are well fitted by an anisotropic two-band BCS s-wave gap function. Our spectroscopic data are confirmed by electronic heat capacity measurements, which also provide evidence for a twin-gap scenario.