This paper studies the minimum bearing error attainable with a linear passive array. Signal and noise are stationary Gaussian processes with arbitrary power spectra, and the noise is assumed to be statistically independent from hydrophone to hydrophone. The Cramér‐Rao technique is used to set a lower bound on the rms bearing error and the results are compared with the bearing error of a slightly modified split‐beam tracker. The latter reaches the lower bound for a two‐element array and comes very close to reaching it for a linear array with an arbitrary number of equally spaced hydrophones. Thus, the modified split‐beam tracker is very nearly optimal for the uniformly spaced array. Comparisons of split‐beam tracker error with the Cramér‐Rao lower bound are also obtained for nonuniform hydrophone spacings.