Using Hubble Space Telescope imaging and Keck spectroscopy, we report the discovery of a very bright, highly magnified (~30 times) Lyman break galaxy (LBG) at z = 3.07 in the field of the massive z = 0.33 cluster MACS J2135.2-0102. The system comprises two high surface brightness arcs with a maximum extent of 3'', bracketing a central object that we identify as a massive early-type galaxy at z = 0.73. We construct a lens model that reproduces the main features of the system using a combination of a galaxy-scale lens and the foreground cluster. We show that the morphological, spectral, and photometric properties of the arcs are consistent with them arising from the lensing of a single ~L LBG. The most important feature of this system is that the lensing magnification results in an apparent magnitude of r = 20.3, making this one of the brightest LBGs known. Such a high magnification provides the opportunity of obtaining very high signal-to-noise ratio (and potentially spatially resolved) spectroscopy of a high-redshift galaxy to study its physical properties. We present initial imaging and spectroscopy demonstrating the basic properties of the system and discuss the opportunities for future observations.