We present a theory of the "autoacceleration" of polymerization rates during free radical polymerization, known as the Trommsdorff or "gel" effect. The starting point is recent theory of polymer-polymer reaction kinetics, according to which the termination rate constant between two macroradicals ("living chains") is dominated by the length N of the shortest chain, k(t) similar to N-(alpha). At lower conversions, when alpha < 1, we show that it is justified to preaverage kt over the living population. Autoacceleration results from a transition to entanglement-dominated kinetics in which short chain domination is so strong as to be unintegrable, i.e., alpha > 1. This invalidates preaveraging. Net termination rates are then dominated by short-long events; long chain mobility is so reduced by entanglements that short mobile chains provide a faster termination mechanism despite their small umbers. This leads to results very different from those of the classical Flory theory. We find polymerization rates are independent of initiation rates R(i), in contrast to the classical root R(i) result, while mean living chain length (N) over bar similar to 1/R(i). Initially, polymer conversion phi grows with a characteristic power or finite time singularity, and for polymerizations above the glass temperature the approach to completion is hyperbolic in time, 1 - phi similar to tau(auto)/t where tau(auto) is the duration of the autoacceleration regime and is independent of R(i). Comparison of theory with a number of experimental measurements is presented.