A \emph{clock} is, from an information-theoretic perspective, a system that
emits time information. One may therefore ask whether the theory of information
imposes any constraints on the maximum precision of clocks. We find that,
indeed, the accuracy of the time information generated by a clock is
fundamentally limited by the clock's size or, more precisely, the dimension~$d$
of its quantum-mechanical state space. Furthermore, compared to a classical
clock, whose evolution is restricted to stochastic jumps between $d$ perfectly
distinguishable classical states, a genuine quantum clock can achieve a
quadratically improved accuracy.