The Ly alpha Reference Sample (LARS) is a substantial program with the Hubble Space Telescope (HST) that provides a sample of local universe laboratory galaxies in which to study the detailed astrophysics of the visibility and strength of the Ly alpha line of neutral hydrogen. Ly alpha is the dominant spectral line in use for characterizing high-redshift (z) galaxies. This paper presents an overview of the survey, its selection function, and HST imaging observations. The sample was selected from the combined GALEX+Sloan Digital Sky Survey catalog at z = 0.028-0.19, in order to allow Ly alpha to be captured with combinations of long-pass filters in the Solar Blind Channel (SBC) of the Advanced Camera for Surveys (ACS) onboard HST. In addition, LARS utilizes H alpha and H beta narrowband and u, b, i broadband imaging with ACS and the Wide Field Camera 3 (WFC3). In order to study galaxies in which large numbers of Ly alpha photons are produced (whether or not they escape), we demanded an H alpha equivalent width W(H alpha) >= 100 angstrom. The final sample of 14 galaxies covers far-UV (FUV, lambda similar to 1500 angstrom) luminosities that overlap with those of high-z Ly alpha emitters (LAEs) and Lyman break galaxies (LBGs), making LARS a valid comparison sample. We present the reduction steps used to obtain the Ly alpha images, including our LARS eXtraction software (LaXs), which utilizes pixel-by-pixel spectral synthesis fitting of the energy distribution to determine and subtract the continuum at Ly alpha. We demonstrate that the use of SBC long-pass-filter combinations increase the signal-to-noise ratio by an order of magnitude compared to the nominal Ly alpha filter available in SBC. To exemplify the science potential of LARS, we also present some first results for a single galaxy, Mrk 259 (LARS #1). This irregular galaxy shows bright and extended (indicative of resonance scattering) but strongly asymmetric Ly alpha emission. Spectroscopy from the Cosmic Origins Spectrograph on board HST centered on the brightest UV knot shows a moderate outflow in the neutral interstellar medium (probed by low ionization stage absorption features) and Ly alpha emission with an asymmetric profile. Radiative transfer modeling is able to reproduce the essential features of the Ly alpha line profile and confirms the presence of an outflow. From the integrated photometry we measure an Ly alpha luminosity of L-Ly alpha= 1.3x10(42) erg s(-1) an equivalent width W(Ly alpha) = 45 angstrom and an FUV absolute magnitude M-FUV = -19.2 (AB). Mrk 259 would hence be detectable in high-z Ly alpha and LBG surveys. The total Ly alpha escape fraction is 12%. This number is higher than the low-z average, but similar to that at z > 4, demonstrating that LARS provides a valid comparison sample for high-z galaxy studies.