  Galaxy color gradients - i.e., spectral energy distributions that vary across
the galaxy profile - will impact galaxy shape measurements when the modeled
point spread function (PSF) corresponds to that for a galaxy with spatially
uniform color. This paper describes the techniques and results of a study of
the expected impact of galaxy color gradients on weak lensing measurements with
the Large Synoptic Survey Telescope (LSST) when the PSF size depends on
wavelength. The bias on cosmic shear measurements from color gradients is
computed both for parametric bulge+disk galaxy simulations and for more
realistic chromatic galaxy surface brightness profiles based on HST V- and
I-band images in the AEGIS survey. For the parametric galaxies, and for the
more realistic galaxies derived from AEGIS galaxies with sufficient SNR that
color gradient bias can be isolated, the predicted multiplicative shear biases
due to color gradients are found to be at least a factor of 2 below the LSST
full-depth requirement on the total systematic uncertainty in the
redshift-dependent shear calibration. The analysis code and data products are
publicly available (https://github.com/sowmyakth/measure_cg_bias).
