  We present and discuss measurements of the gas-phase metallicity gradient in
gravitationally lensed galaxies at z=2.0-2.4 based on adaptive optics-assisted
imaging spectroscopy with the Keck II telescope. Through deep exposures we have
secured high signal to noise data for four galaxies with well-understood
kinematic properties. Three galaxies with well-ordered rotation reveal
metallicity gradients in the sense of having lower gas-phase metallicities at
larger galactocentric radii. Two of these display gradients much steeper than
found locally, while a third has one similar to that seen in local disk
galaxies. The fourth galaxy exhibits complex kinematics indicative of an
ongoing merger and reveals an "inverted" gradient with lower metallicity in the
central regions. By comparing our sample to similar data in the literature for
lower redshift galaxies, we determine that, on average, metallicity gradients
must flatten by a factor of 2.6 +/- 0.9 between z=2.2 and the present epoch.
This factor is in rough agreement with the size growth of massive galaxies
suggesting that inside-out growth can account for the evolution of metallicity
gradients. Since the addition of our new data provides the first indication of
a coherent picture of this evolution, we develop a simple model of chemical
evolution to explain the collective data. We find that metallicity gradients
and their evolution can be explained by the inward radial migration of gas
together with a radial variation in the mass loading factor governing the ratio
of outflowing gas to the local star formation rate. Average mass loading
factors of \lsim 2 are inferred from our model in good agreement with direct
measurements of outflowing gas in z \simeq 2 galaxies.
