  We present a natural scenario for obtaining an open universe ($\Omega _0<1$)
through inflation. In this scenario, there are two epochs of inflationary
expansion---an epoch of `old inflation,' during which the inflaton field is
stuck in a false vacuum, followed by an epoch of `new inflation,' during which
the inflaton field slowly rolls toward its true minimum. During the first
epoch, inflation solves the smoothness and horizon problems. Then an open
universe (with negative spatial curvature) is created by the nucleation of a
single bubble. In effect $\Omega$ is instantaneously `reset' to zero. During
the subsequent `new' inflation $\Omega$ rises toward unity. The value of
$\Omega$ today is calculable in terms of the parameters of the potential, and
we show that obtaining values significantly different from zero or unity
(though within the range $0<\Omega <1$) does not require significant fine
tuning. We compute the spectrum of density perturbations by evolving the
Bunch-Davies vacuum modes across the bubble wall into its interior.
