Colloidal quantum dot solar cells have shown remarkable improvements in performance during the last few years. Until now, mostly Pb- or Cd-based nanocrystals were used as absorber material, which might limit the potential application of nanocrystal solar cells due to toxicity issues. A promising, potentially less-toxic alternative are CuInS2 (CIS) nanocrystals. Here, we report about the realization of solar cells based on a heterojunction formed by solution-producible layers of colloidal CIS and ZnO nanocrystals. Device performance was found to be sensitive to illumination conditions, i.e., the presence of UV light. Although, power conversion efficiencies remain limited in this work, we modeled the possible photocurrents and show that the CIS nanocrystals have a high potential for light-harvesting in quantum dot solar cells.