HD 15144 (HR 710) is a single-line spectroscopic binary Ap star with a period of 3^00, which has a variable magnetic field but no obvious variations in line strengths or light. New spectrograms are combined with previous observations by Babcock to derive a probable magnetic period of 15?9. An apparent rotational velocity of 7.7 km s -1 is obtained and combined with elements of the orbit to estimate the mass of the secondary. The spectrum of the secondary cannot be detected between 3800 Â and 6700 Â. The most plausible model for the system appears to be one in which the rotation period of the Ap star is 3?00, the system is seen nearly pole-on, the secondary is a subluminous star of approximately 1.2 solar masses, and the magnetic variation is due to intrinsic changes of the field strength or geometry. An alternative model assumes that the rotation period of the Ap star is 15?9 days, the system is seen edge-on, the mass of the secondary is 0.2 solar mass, and the magnetic variation is due to rotation with a fixed, but very asymmetric, magnetic field geometry.