  The Crab nebula pulsar was observed in 2009 January and December with a novel
very fast optical photon counter, Iqueye, mounted at the ESO 3.5 m New
Technology Telescope. Thanks to the exquisite quality of the Iqueye data, we
computed accurate phase coherent timing solutions for the two observing runs
and over the entire year 2009. Our statistical uncertainty on the determination
of the phase of the main pulse and the rotational period of the pulsar for
short (a few days) time intervals are $\approx 1 \, \mu$s and ~0.5 ps,
respectively. Comparison with the Jodrell Bank radio ephemerides shows that the
optical pulse leads the radio one by ~240 $\mu$s in January and ~160 $\mu$s in
December, in agreement with a number of other measurements performed after
1996. A third-order polynomial fit adequately describes the spin-down for the
2009 January plus December optical observations. The phase noise is consistent
with being Gaussian distributed with a dispersion $\sigma$ of $\approx 15 \,
\mu$s in most observations, in agreement with theoretical expectations for
photon noise-induced phase variability.
