  We report new Chandra observations of one of the few Galactic supernova
remnants whose X-ray spectrum is dominated by nonthermal synchrotron radiation,
G330.2+1.0. We find that between 2006 and 2017, some parts of the shell have
expanded by about 1%, giving a free-expansion (undecelerated) age of about 1000
yr, and implying shock velocities there of 9000 km/s for a distance of 5 kpc.
Somewhat slower expansion is seen elsewhere around the remnant periphery, in
particular in compact knots. Because some deceleration must have taken place,
we infer that G330.2+1.0 is less than about 1000 yr old. Thus, G330.2+1.0 is
one of only four Galactic core-collapse remnants of the last millennium. The
large size, low brightness, and young age require a very low ambient density,
suggesting expansion in a stellar-wind bubble. We suggest that in the east,
where some thermal emission is seen and expansion velocities are much slower,
the shock has reached the edge of the cavity. The high shock velocities can
easily accelerate relativistic electrons to X-ray-emitting energies. A few
small regions show highly significant brightness changes by 10% to 20%, both
brightening and fading, a phenomenon previously observed in only two supernova
remnants, indicating strong and/or turbulent magnetic fields.
