Selective listening in competing-talker situations (restaurants, parties, etc.) is an extraordinarily difficult task for many people. For individuals with hearing loss, this difficulty can be so extreme that it seriously impedes communication and participation in daily life. Directional filtering is one of the only proven ways to improve speech understanding in competition, and most hearing devices now incorporate some kind of directional technology, although real-world benefits are modest, and many approaches fail in competing-talker situations. We recently developed a biologically inspired algorithm that is capable of very narrow spatial tuning and can isolate one talker from a mixture of talkers. The algorithm is based on a hierarchical network model of the auditory system, in which binaural sound inputs drive populations of neurons tuned to specific spatial locations and frequencies, and the spiking responses of neurons in the output layer are reconstructed into audible waveforms. Here we evaluated the algorithm in a group of adults with sensorineural hearing loss, using a challenging competing-talker task. The biologically inspired algorithm led to robust intelligibility gains under conditions in which a standard beamforming approach failed. The results provide compelling support for the potential benefits of biologically inspired algorithms for assisting individuals with hearing loss in cocktail party situations.