The pace of materials discovery for heterogeneous catalysts and electrocatalysts could, in principle, be accelerated by the development of efficient computational screening methods. This would require an integrated approach, where the catalytic activity and stability of new materials are evaluated and where predictions are benchmarked by careful synthesis and experimental tests. In this contribution, we present a density functional theory-based, high-throughput screening scheme that successfully uses these strategies to identify a new electrocatalyst for the hydrogen evolution reaction (HER). The activity of over 700 binary surface alloys is evaluated theoretically; the stability of each alloy in electrochemical environments is also estimated. BiPt is found to have a predicted activity comparable to, or even better than, pure Pt, the archetypical HER catalyst. This alloy is synthesized and tested experimentally and shows improved HER performance compared with pure Pt, in agreement with the computational screening results.