Hubble Space Telescope images of high-redshift galaxies selected via color and photometric redshifts are used to examine the size and axial-ratio distribution of galaxies as a function of redshift at lookback times t > 8 Gyr . These parameters are measured at rest-frame UV wavelengths ( 1200 < \lambda < 2000 Å ) on images with a rest-frame resolution of less than 0.8 kpc . Galaxy radii are found to scale with redshift approximately as Hubble parameter H ^ { -1 } ( z ) . This is in accord with the theoretical expectation that the typical sizes of the luminous parts of galaxies should track the expected evolution in the virial radius of dark-matter halos . The mean ratio of semi-major to semi-minor axis for a bright well-resolved sample of galaxies at z \sim 4 is b / a = 0.65 , suggesting that these Lyman break galaxies are not drawn from a spheroidal population . However the median concentration index of this sample is C = 3.5 , which is closer to the typical concentration indices , C \sim 4 , of nearby elliptical galaxies than to the values , C < 2 for local disk galaxies of type Sb and later .