  Using HST/ACS observations, we measure the color gradients of 3248 galaxies
in the GOODS-South field out to z~3 and i_{AB}<25.5 and characterize their
dependence on galaxy properties (luminosity, apparent magnitude, galaxy size,
redshift and morphological type). The color gradient is measured by the
difference of v-i color outside (R_{50}<r<2R_{50}) and inside the half light
radius. The gradient shows little evolution with redshift up to z~1 but
increases from z~1 to z~2 before flattening out. It also increases with
apparent magnitude, with a median value of 0.24 magnitudes at i_{AB}~25.5. It
has a strong color dependence, with the bluest galaxies (in terms of observed
color) having cores that are bluer relative to their outskirts. We probe the
redshift evolution by stacking galaxies and measuring the radial variation of
v-i color within them. At low redshifts (z<0.5), the centres of galaxies
(r<R_{50}) are slightly redder than their outskirts (1.5R_{50}<r<2R_{50}).
Galaxies at z~1 and -22.0<M_I<-21.0 are bluer in their cores by 0.1 magnitudes,
on average, compared to their outskirts. For z>1, galaxies show increasingly
bluer cores while the color of the outskirts does not change as rapidly. At
z~2.5 and -22.0<M_I<-21.0, we observe a difference, on average, of 0.4
magnitudes between the centre and the outskirts. The observed color gradients
may indicate that strong star formation in galaxies at z>=2 is concentrated in
their central regions. These color gradients and their dependence on galaxy
properties could also have a significant impact on shear measurements in
upcoming weak lensing cosmological surveys.
