  Using X-ray data from the Rossi X-Ray Timing Explorer (RXTE), we report the
pulse timing results of the accretion powered high mass X-ray binary (HMXRB)
pulsar 4U 1907+09 covering a time span of almost two years. We measured three
new pulse periods in addition to the previously measured four pulse periods. We
are able to connect pulse arrival times in phase for more than a year. The
source has been spinning down almost at a constant rate with a spin down rate
of
  \dot \nu = (-3.54 \pm 0.02) \times 10^{-14} Hz s ^{-1} for more than
  15 years. Residuals of pulse arrival times yield a very low level of random
walk noise strengths
  \sim 2 \times 10^{-20} rad ^{2} sec ^{-3} on a time scale of 383 days, which
is four decades lower than that of the HMXRB pulsar Vela X-1. The noise
strength is only a factor of 5 greater than that of the low mass X-ray binary
pulsar (LMXRB) 4U 1626-67. The low level of the timing noise and the very
stable spin down rate of 4U 1907+09 makes this source unique among the HMXRBs,
providing another example, in addition to 4U 1626-67, of long term quiet spin
down from an accreting source. These examples show that the extended quiet spin
down episodes observed in the anomalous X-ray pulsars (AXPs) pulsars 1RXS
J170849.0-400910 and 1E 2259+586 do not necessarly imply that these sources are
not accreting pulsars.
