Context. The dwarf planet Eris (2003 UB313, formerly known also as "Xena") is the largest KBO discovered up to now. Despite being larger than Pluto and having many similarities to it, it has not been possible so far to detect any significant variability in its light curve, preventing the determination of its period and axial ratio. Aims. We attempt to assess the level of variability of the Eris light curve by determining its BVRI photometry with a target accuracy of 0.03 mag/frame in R and a comparable or better stability in the calibration. This cannot be explained by known systematics, background objects, or some periodical variation with periods less than two days in the lightcurve. The same applies to B, V and to a lesser extent to I, due to larger errors. Conclusions. In analogy with Pluto and if confirmed by future observations, this "long term" variability might be ascribed to a slow rotation of Eris, with periods longer than 5 days, or to the effect of its unresolved satellite "Dysnomea", which may contribute for ≈0.02 mag to the total brightness.