We present evidence that bandgap narrowing at the heterointerface may be a major cause of the large open circuit voltage deficit of Cu2ZnSnS4/CdS solar cells. Bandgap narrowing is caused by surface states that extend the Cu2ZnSnS4valence band into the forbidden gap. Those surface states are consistently found in Cu2ZnSnS4, but not in Cu2ZnSnSe4, by first-principles calculations. They do not simply arise from defects at surfaces but are an intrinsic feature of Cu2ZnSnS4 surfaces. By including those states in a device model, the outcome of previously published temperature-dependent open circuit voltage measurements on Cu2ZnSnS4 solar cells can be reproduced quantitatively without necessarily assuming a cliff-like conduction band offset with the CdS buffer layer. Our first-principles calculations indicate that Zn-based alternative buffer layers are advantageous due to the ability of Zn to passivate those surface states. Focusing future research on Zn-based buffers is expected to significantly improve the open circuit voltage and efficiency of pure-sulfide Cu2ZnSnS4 solar cells.