For multivariate regression with a symmetric disturbance distribution, the error in the least absolute residuals estimator is approximately multivariate normally distributed with mean zero and variance matrix λ2(X′X)−1, where X is the matrix of K explanatory variables and T observations, and λ2/T is the variance of the median of a sample of size T from the disturbance distribution. The approximate sampling theory is validated by extensive Monte Carlo studies, and some directions of possible refinement emerge.