This article shows that portfolio constraints can give rise to rational asset pricing bubbles in equilibrium even if there are unconstrained agents in the economy who can benefit from the induced limited arbitrage opportunities. Furthermore, it is shown that bubbles can lead to both multiplicity and real indeterminacy of equilibria. The general results are illustrated by two explicitly solved examples where seemingly innocuous portfolio constraints make bubbles a necessary condition for the existence of an equilibrium. (c) 2012 Elsevier Inc. All rights reserved.