We have discovered a 7.1 h period and eclipses in the X‐ray emission from MXB 1659‐29. MXB 1659‐29 is the first burst source to show persistent, regular eclipses. Irregular variability is observed during approximately 25% of the cycle (∼1.5 hours) immediately preceding the eclipse, which is only 15 minutes in duration. We derive limits to the mass of the binary companion to the X‐ray emitting neutron star, and argue that the companion is less massive than the canonical prediction for Roche lobe filling main sequence stars.