Surprising observations of radial velocity variations and spectral type of the low-mass X-ray binary (LMXRB) 4U 2129 + 47 made from June 1987 to October 1988 are reported. Shifts in the mean radial velocity, the lack of variations in the orbital period, and the anomalous spectral type suggest that this system is a hierarchical triple with an inner boundary consisting of an LMXRB with a 5.24 hr period and an F7 V star in a much larger orbit around the inner binary. A necessary consequence of such a triple would be a cycle of about 45 yr in the mean eccentricity of the inner binary, which is consistent with the pattern of on and off states that have been observed since the 1930s.