  We obtain sharp estimates for certain trilinear oscillatory integrals. In
particular, we extend Phong and Stein's seminal result to a trilinear setting.
This result partially answers a question raised by Christ, Li, Tao and Thiele
concerning the sharp estimates for certain multilinear oscillatory integrals.
The method in this paper relies on a self-contained algorithm of resolution of
singularities in $\mathbb R^2$, which may be of independent interest.
