We compare the conductance of an undoped graphene sheet with a small region subject to an electrostatic gate potential for the cases that the dynamics in the gated region is regular (disc-shaped region) and classically chaotic (stadium). For the disc, we find sharp resonances that narrow upon reducing the area fraction of the gated region. We relate this observation to the existence of confined electronic states. For the stadium, the conductance loses its dependence on the gate voltage upon reducing the area fraction of the gated region, which signals the lack of confinement of Dirac quasiparticles in a gated region with chaotic classical electron dynamics. © 2009 The American Physical Society.