  We report on a long-term monitoring campaign of 1E 1841-045, the 12-s
anomalous X-ray pulsar and magnetar candidate at the center of the supernova
remnant Kes 73. We have obtained approximately monthly observations of the
pulsar with the Rossi X-ray Timing Explorer spanning over two years, during
which time 1E 1841-045 is found to be rotating with sufficient stability to
derive a phase-connected timing solution. A linear ephemeris is consistent with
observations of the pulse period made over the last 15 yrs with the Ginga,
ASCA, XTE, & SAX observatories. Phase residuals suggest the presence of "timing
noise", as is typically observed from young radio pulsars. These results
confirm a rapid, constant spin-down for the pulsar, which continues to maintain
a steady flux; this is inconsistent with most accretion scenarios.
