We calculate the magnetic moment (“persistent current”) in a strongly correlated electron system - a Wigner crystal - in a one-dimensional ballistic ring (quantum ring). The flux- and temperature dependence of the persistent current is shown to be essentially the same as for a system of non-interacting electrons. In contrast, by incorporating into the ring geometry a tunnel barrier, that pins the Wigner crystal, the current is suppressed and its temperature dependence is drastically changed. The competition between two temperature effects - a reduced barrier height for macroscopic tunneling and a loss of quantum coherence - results in a sharp peak in the temperature dependence, which for a rigid Wigner crystal appears at T ~ 0.5hs/L, (s is the sound velocity of the Wigner crystal, L is the length of the ring).