A first-principles calculation of the linewidth of a distributed-feedback (DFB) semiconductor laser is presented. The treatment involves a detailed account of the longitudinal power distribution in the laser cavity, including the effects of spontaneous emission. The result is expressed in terms of output power, cavity length, and a normalised function of the product of coupling coefficient and length. For large values of this latter product (greater tharf about five), the linewidth varies approximately as the inverse square of the coupling coefficient and as the inverse cube of the cavity length.