  We investigate a one-dimensional S=1 antiferromagnetic Heisenberg model
coupled to a lattice distortion by a quantum Monte Carlo method. Investigating
the ground state energy of the static bond-alternating chain, we find that the
instability to a dimerized chain depends on the value of the spin-phonon
coupling, unlike the case of S=1/2. The spin state is the dimer state or the
uniform Haldane state depending on whether the lattice distorts or not,
respectively. At an intermediate value of the spin-phonon coupling, we find the
first-order transition between the two states. We also find the coexistence of
the two states.
