We present a study of the type IIn supernova (SN) 2005gl, in the relatively nearby (d~66 Mpc) galaxy NGC 266. Photometry and spectroscopy of the SN indicate it is a typical member of its class. Pre-explosion Hubble Space Telescope (HST) imaging of the location of the SN, along with a precise localization of this event using the Laser-Guide-Star assisted Adaptive Optics (LGS-AO) system at Keck Observatory, are combined to identify a luminous (M_V=-10.3) point source as the possible progenitor of SN 2005gl. If the source is indeed a single star, it was likely a member of the class of luminous blue variable stars (LBVs). This finding leads us to consider the possible general association of SNe IIn with LBV progenitors. We find this is indeed supported by observations of other SNe, and the known properties of LBV stars. For example, we argue that should the prototypical Galactic LBV eta Carina explode in a phase similar to its current state, it will likely produce a type IIn SN. We discuss our findings in the context of current ideas about the evolution of massive stars, and review the census of SNe with identified progenitors. We introduce the concept of the progenitor-SN map as a convenient means to discuss the present status and future prospects of direct searches for SN progenitors. We conclude that this field has matured considerably in recent years, and the transition from anecdotal information about rare single events to robust associations of progenitor classes with specific SN types has already begun.