A pair of chaotic dynamical systems can synchronize when loosely coupled in a variety of ways. It is suggested that the synchronization phenomenon, with one system representing ``truth" and the other system representing ``model," provides a new approach to data assimilation in high-dimensional systems. One is led to search for low-dimensional subspaces through which the two systems can be synchronously coupled, such as a subspace defined by a small number of local bred vectors. It is argued that the synchronization approach differs qualitatively from any of the standard approaches to data assimilation. A stochastic differential equation (SDE) is formulated for continuous data assimilation in a coupled pair of linearized systems, with observation error taken to correspond to noise in the coupling channel. Background error is computed as the spread of the probability distribution function (PDF) that is a stationary solution of the corresponding Fokker-Planck equation. The coupling in the linearized SDE that is optimal for synchronization, in the sense of giving the smallest PDF spread, reproduces the standard data assimilation recipes used in 3DVar and Kalman Filtering. The analysis is used to motivate a suggestion that the synchronization-based definition of the optimal coupling for the full nonlinear model will improve upon Kalman Filtering in the vicinity of regime transitions.