In this paper we describe a speech enhancement system which is based on an adaptive beamformer and which can significantly enhance cocktail party speech. This beamformer is effective in suppressing both stationary and non-stationary interferences and is therefore suited as preprocessor for a much wider range of speech recognition systems than any single channel noise suppression scheme. The underlying structure is a steered Griffiths-Jim beamformer, with an added switch for speech detection. Experiments were performed in a reverberant room with a 4 microphone array. With a talker, one to several meters away from the array, typical SNR improvements range from 4 to 14 dB. This is enough to extend the operating range of current speech recognition into many every day circumstances.