We develop a general nonlinear Luttinger liquid theory to describe the dynamics of one-dimensional quantum critical systems at low temperatures. To demonstrate the predictive power of our theory we compare results for the autocorrelation G(t) in the XXZ chain with numerical density-matrix renormalization group data and obtain excellent agreement. Our calculations provide, in particular, direct evidence that G(t) shows a diffusion-like decay, $G(t)\sim 1/\sqrt{t},$ in sharp contrast to the exponential decay in time predicted by conventional Luttinger liquid theory.
