We present the first concrete evidence for the classical stability of vortons, circular cosmic string loops stabilized by the angular momentum of the charge and current trapped on the string. We begin by summarizing what is known about vorton solutions and, in particular, their analytic stability with respect to a range of radial and nonradial perturbations. We then discuss numerical results of vorton simulations in a full 3D field theory, that is, Witten's original bosonic superconducting string model with a modified potential term. For specific parameter values, these simulations demonstrate the long-term stability of sufficiently large vorton solutions created with an elliptical initial ansatz.