  We generalize the effective field theory of single clock inflation to include
dissipative effects. Working in unitary gauge we couple a set of composite
operators in the effective action which is constrained solely by invariance
under time-dependent spatial diffeomorphisms. We restrict ourselves to
situations where the degrees of freedom responsible for dissipation do no
contribute to the density perturbations at late time. The dynamics of the
perturbations is then modified by the appearance of `friction' and noise terms,
and assuming certain locality properties for the Green's functions of these
composite operators, we show that there is a regime characterized by a large
friction term \gamma >> H in which the \zeta-correlators are dominated by the
noise and the power spectrum can be significantly enhanced. We also compute the
three point function <\zeta\zeta\zeta> for a wide class of models and discuss
under which circumstances large friction leads to an increased level of
non-Gaussianities. In particular, under our assumptions, we show that strong
dissipation together with the required non-linear realization of the symmetries
implies |f_NL| ~ \gamma/(c_s^2H) >> 1. As a paradigmatic example we work out a
variation of the `trapped inflation' scenario with local response functions and
perform the matching with our effective theory. A detection of the generic type
of signatures that result from incorporating dissipative effects during
inflation, as we describe here, would teach us about the dynamics of the early
universe and also extend the parameter space of inflationary models.
