In this paper, we consider the problem of minimizing expected shortfall for a contingent claim in a continuous-time, multiasset financial market in the presence of proportional transaction costs. By generalizing the convex duality technique of Cvitanic [SIAM J. Control. Optim., 38 (2000), pp. 1050-1066] to the case of multivariate contingent claim, we establish the existence of an optimal trading strategy and describe it in terms of an appropriate dual optimization problem.