  An uncertainty relation for the number and phase of a single-mode field state
is derived. It is then used to find a lower bound on the phase noise of a
classical state. Any state that violates this condition is nonclassical. An
example of such a nonclassical state is presented. Because a nonclassical state
can have less phase noise than a classical state with the same average photon
number, nonclassical states can play a role in the measurement of small phase
shifts.
