  We present a Chandra observation of the H II region RCW89. The nebula lies on
10' north from the central pulsar PSR B1509-58, and it has been suggested that
the nebula is irradiated by the pulsar jet. We performed a spectral analysis of
the seven brightest emitting regions aligned in a ``horse-shoe'' shape, and
found that the temperature of the knots increases along the ``horse-shoe'' in
the clockwise direction, while, in contrast, the ionization parameter
decreases. This strongly supports a picture of energy transfer via the
precessing pulsar jet. We examined the energy budget assuming that RCW89 is
powered by the pulsar jet, and confirmed that the pulsar rotational energy loss
is sufficient to drive the nebula. The rate of energy injection into RCW89 by
the jet was estimated from the synchrotron radiation flux. We obtained a
heating time-scale of 1400 yr, which is consistent with the pulsar
characteristic age of 1700 yr. To explain the temperature gradient, we discuss
the cooling process for plasma clouds in RCW89. We argue that the plasma clouds
can be cooled down by the adiabatic expansion within 70 yr, and form the
temperature gradient reflecting the sequential heating by the precessing pulsar
jet. We also determined the velocities of the individual plasma clouds by
spectral fitting. The plasma clouds in RCW89 are moving away at 240 ~ 860 km/s,
which constrains the inclination angle of the pulsar spin axis i > 50 degree
and the expanding velocity of the shell as v > 1100 km/s.
