We present new visible and infrared observations of the hot Jupiter Kepler-7b to determine its atmospheric properties. Our analysis allows us to (1) refine Kepler-7b's relatively large geometric albedo of Ag = 0.35 ± 0.02, (2) place upper limits on Kepler-7b thermal emission that remains undetected in both Spitzer bandpasses and (3) report a westward shift in the Kepler optical phase curve. We argue that Kepler-7b's visible flux cannot be due to thermal emission or Rayleigh scattering from H2 molecules. We therefore conclude that high altitude, optically reflective clouds located west from the substellar point are present in its atmosphere. We find that a silicate-based cloud composition is a possible candidate. Kepler-7b exhibits several properties that may make it particularly amenable to cloud formation in its upper atmosphere. These include a hot deep atmosphere that avoids a cloud cold trap, very low surface gravity to suppress cloud sedimentation, and a planetary equilibrium temperature in a range that allows for silicate clouds to potentially form in the visible atmosphere probed by Kepler. Our analysis does not only present evidence of optically thick clouds on Kepler-7b but also yields the first map of clouds in an exoplanet atmosphere.