Observations with the Fermi Large Area Telescope (LAT) of the gamma-ray source 4FGL J1702.7−5655, previously classified as a candidate millisecond pulsar, show highly significant modulation at a period of 0.2438033 days (∼5.85 hr). Further examination of the folded light curve indicates the presence of narrow eclipses, suggesting that this is a redback binary system. An examination of the long-term properties of the modulation over 13 years of LAT observations indicates that the orbital modulation of the gamma rays changed from a simple eclipse before early 2013 to a broader, more easily detected quasi-sinusoidal modulation. In addition, the time of the eclipse shifts to ∼0.05 later in phase. This change in the orbital modulation properties, however, is not accompanied by a significant overall change in gamma-ray flux or spectrum. The quasi-sinusoidal component peaks ∼0.5 out of phase with the eclipse, which would indicate inferior conjunction of the compact object in the system. Swift X-ray Telescope observations reveal a possible X-ray counterpart within the LAT error ellipse. However, radio observations obtained with the Australia Telescope Compact Array do not detect a source in the region. 4FGL J1702.7−5655 appears to have changed its state in 2013, perhaps related to changes in the intrabinary shock in the system. We compare the properties of 4FGL J1702.7−5655 to those of other binary millisecond pulsars that have exhibited orbital modulation in gamma-rays.