  We consider the operator $$\sL f(x)=\tfrac12 \sum_{i,j=1}^\infty
a_{ij}(x)\frac{\del^2 f}{\del x_i \del x_j}(x)-\sum_{i=1}^\infty \lam_i x_i
b_i(x) \frac{\del f}{\del x_i}(x).$$ We prove existence and uniqueness of
solutions to the martingale problem for this operator under appropriate
conditions on the $a_{ij}, b_i$, and $\lam_i$. The process corresponding to
$\sL$ solves an infinite dimensional stochastic differential equation similar
to that for the infinite dimensional Ornstein-Uhlenbeck process.
