  We present time-dependent axisymmetric magnetohydrodynamic simulations of the
interaction of a relativistic magnetized wind produced by a proto-magnetar with
a surrounding stellar envelope, in the first $\sim 10$ seconds after core
collapse. We inject a super-magnetosonic wind with $\dot E = 10^{51}$ ergs
s$^{-1}$ into a cavity created by an outgoing supernova shock. A strong
toroidal magnetic field builds up in the bubble of plasma and magnetic field
that is at first inertially confined by the progenitor star. This drives a jet
out along the polar axis of the star, even though the star and the magnetar
wind are each spherically symmetric. The jet has the properties needed to
produce a long-duration gamma-ray burst (GRB). At $\sim 5$ s after core bounce,
the jet has escaped the host star and the Lorentz factor of the material in the
jet at large radii $\sim 10^{11}$ cm is similar to that in the magnetar wind
near the source. Most of the spindown power of the central magnetar escapes via
the relativistic jet. There are fluctuations in the Lorentz factor and energy
flux in the jet on $\sim 0.01-0.1$ second timescale. These may contribute to
variability in GRB emission (e.g., via internal shocks).
