  Tracy-Widom and Baik-Rains distributions appear as universal limit
distributions for height fluctuations in the one-dimensional
Kardar-Parisi-Zhang (KPZ) \textit{stochastic} partial differential equation
(PDE). We obtain the same universal distributions in the spatiotemporally
chaotic, nonequilibrium, but statistically steady state (NESS) of the
one-dimensional Kuramoto-Sivashinsky (KS) \textit{deterministic} PDE, by
carrying out extensive pseudospectral direct numerical simulations to obtain
the spatiotemporal evolution of the KS height profile $h(x,t)$ for different
initial conditions. We establish, therefore, that the statistical properties of
the 1D KS PDE in this state are in the 1D KPZ universality class.
