Simultaneous UBVRI photopolarimetric observations of the highly variable BL Lac object OJ 287 have been obtained on six nights. The polarization and position angle, as well as their wavelength dependence, have been found to be variable from night to night and also on a timescale of a few hours. During the first three consecutive nights, a clear anticorrelation existed between the flux density and the degree of polarization such that when the object brightened the polarization decreased. During the same nights, a possible rotation in the p(x)p(y) plane was noted. These observations are not easily explained by a single component synchrotron model; a better explanation would be a relativistic jet pointing toward earth, with shocked, highly polarized clumps rotating inside it.