We report on new imaging observations of the Lyman alpha emission line ( Ly \alpha ) , 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 Ly \alpha , H \alpha , and the far ultraviolet continuum . We show that Ly \alpha is emitted on scales that systematically exceed those of the massive stellar population and recombination nebulae : as measured by the Petrosian 20 percent radius , R _ { \mathrm { P } 20 } , Ly \alpha radii are larger than those of H \alpha by factors ranging from 1 to 3.6 , with an average of 2.4 . The average ratio of Ly \alpha -to-FUV radii is 2.9 . This suggests that much of the Ly \alpha light is pushed to large radii by resonance scattering . Defining the Relative Petrosian Extension of Ly \alpha compared to H \alpha , \xi _ { \mathrm { Ly } \alpha } = R _ { \mathrm { P } 20 } ^ { \mathrm { Ly } \alpha } / R _ { \mathrm { P } 20 } ^ { \mathrm { H } \alpha } , we find \xi _ { \mathrm { Ly } \alpha } to be uncorrelated with total Ly \alpha luminosity . However \xi _ { \mathrm { Ly } \alpha } 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 Ly \alpha photons throughout the interstellar medium and drive a large extended Ly \alpha halo .