The global SARS-CoV-2 pandemic started late 2019 and currently continues unabated. The lag-time for developing vaccines means it is of paramount importance to be able to quickly develop and repurpose therapeutic drugs. Protein-based biosensors allow screening to be performed using routine molecular laboratory equipment without a need for expensive chemical reagents. Here we present a biosensor for the 3-chymotrypsin-like cysteine protease from SARS-CoV-2, comprising a FRET-capable pair of fluorescent proteins held in proximity by a protease cleavable linker. We demonstrate the utility of this biosensor for inhibitor discovery by screening 1280 compounds from the Library of Pharmaceutically Active Compounds collection. The screening identified 65 inhibitors, with the 20 most active exhibiting sub-micromolar inhibition of 3CL(pro) in follow-up EC50 assays. The top hits included several compounds not previously identified as 3CL(pro) inhibitors, in particular five members of a family of aporphine alkaloids that offer promise as new antiviral drug leads.