We present a new microphone array calibration algorithm specifically designed for speech recognition. Currently, microphone-array-based speech recognition is performed in two independent stages: array processing, and then recognition. Array processing algorithms designed for speech enhancement process the waveforms before recognition. These systems make the assumption that the best array processing methods will result in the best recognition performance. However, recognition systems interpret a set of features extracted from the speech waveform, not the waveform itself. In our calibration method, the filter parameters of a filter-and-sum array processing scheme are optimized to maximize the likelihood of the recognition features extracted from the resulting output signal. By incorporating the speech recognition system into the design of the array processing algorithm, we are able to achieve improvements in word error rate of up to 37% over conventional array processing methods on both simulated and actual microphone array data.