We report the results of a long campaign of time-series photometry on the nova-like variable UX Ursae Majoris during 2015. It spanned 150 nights, with ~1800 hours of coverage on 121 separate nights. The star was in its normal `high state near magnitude V=13, with slow waves in the light curve and eclipses every 4.72 hours. Remarkably, the star also showed a nearly sinusoidal signal with a full amplitude of 0.44 mag and a period of 3.680 +/- 0.007 d. We interpret this as the signature of a retrograde precession (wobble) of the accretion disc. The same period is manifest as a +/-33 s wobble in the timings of mid-eclipse, indicating that the discs centre of light moves with this period. The star also showed strong `negative superhumps at frequencies w_orb+N and 2w_orb+N, where w_orb and N are respectively the orbital and precession frequencies. It is possible that these powerful signals have been present, unsuspected, throughout the more than 60 years of previous photometric studies.
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