We study the dependence of Lyα escape from galaxies on UV continuum size and luminosity using a sample of 40 Green Pea (GP) galaxies, which are the best local analogs of high-redshift Lyα emitters (LAEs). We use the high angular resolution Cosmic Origins Spectrograph near-ultraviolet images from the Hubble Space Telescope to measure the UV size and luminosity. Like most galaxies the GPs show a log-normal size distribution. They also show a positive correlation between size and UV-continuum luminosity. The slope of the size-continuum luminosity relation for GPs is consistent with those of continuum-selected star-forming galaxies at low and high redshifts. A distinctive feature of GPs is a very compact typical radius of 0.31 kpc with a population spread (1σ) of 0.19 kpc. The peak of the size distribution and the intercept of the size-luminosity relation of GPs are noticeably smaller than those of continuum-selected star-forming galaxies at similar redshifts. There are statistically significant anti-correlations found between the circularized half-light radius, the Lyα equivalent width, and the Lyα escape faction, suggesting that small UV-continuum radii are crucial for Lyα emission. GPs and high-redshift LAEs have similar sizes, once spatial resolution effects are properly considered. Our results show that a compact size is crucial for escape of Lyα photons, and that Lyα emitters show constant characteristic size independent of their redshift.