We present a synthesis technique for circular arrays of antennas that allows to determine an array pattern having side lobes of assigned level and one main beam whose width does not exceed a prescribed threshold. The method develops in two steps, At first it generates, by means of a suitable Chebyshev polynomial, a reference pattern satisfying the conditions imposed by the synthesis problem. Subsequently, it determines the solution as the array pattern minimizing the mean-square distance from the reference pattern. Numerical examples show the effectiveness of the method.