We report on new imaging observations of the Lyman alpha emission line (Lya), performed with the Hubble Space Telescope, that comprise the backbone of the Lyman alpha Reference Sample (LARS). We present images of 14 starburst galaxies at redshifts 0.028 < z < 0.18 in continuum-subtracted Lya, Halpha, and the far ultraviolet continuum. We show that Lya is emitted on scales that systematically exceed those of the massive stellar population and recombination nebulae: as measured by the Petrosian 20 percent radius, RP20, Lya radii are larger than those of Halpha by factors ranging from 1 to 3.6, with an average of 2.4. The average ratio of Lya-to-FUV radii is 2.9. This suggests that much of the Lya light is pushed to large radii by resonance scattering. Defining the "Relative Petrosian Extension" of Lya compared to Halpha, \xi_ext = RP20_Lya / RP20_Ha, we find \xi_ext to be uncorrelated with total Lya luminosity. However \xi_ext is strongly correlated with quantities that scale with dust content, in the sense that a low dust abundance is a necessary requirement (although not the only one) in order to spread Lya photons throughout the interstellar medium and drive a large extended Lya halo.