We study random nonlinear perturbations of a PDE and prove that a large deviation principle holds. To this purpose we introduce a class of quasi-linear parabolic equations defined on a separable Hilbert space depending on a small parameter in front of the second order term. Studying the nonlinear semigroup associated with such equation, we are able to find sufficient regular solutions to derive the large deviations principle and we give also an explicit description of the action functional, as in the finite dimensional case. This result is obtained in collaboration with S. Cerrai (University of Maryland) and G. Tessitore (University Milano Bicocca).