  Phase diagram of S=1 XXZ chain in a staggered magnetic field is obtained
numerically. The Berezinskii-Kosterlitz-Thouless transition between the XY and
the antiferromagnetic phases is studied by the level-spectroscopy. Moreover we
find that there is no distinction between the Haldane and the antiferromagnetic
phases, since the Gaussian critical line does not appear, in contrast to the
$S=1/2$ case. It is expected that some hidden $Z_2\times Z_2$ symmetry breaking
happens not only in the Haldane phase but also in the antiferromagnetic one.
