This 1972 pop ballad by American rock band Big Star is the song that plays while Rory and Dean walk through Stars Hollow drinking coffee.
It is from their debut album #1 Record, and although never released as a single, is recognised as one of the greatest songs of all time. Thirteen is about adolescent love, and even mentions getting tickets for a school dance, just as Rory and Dean did.
The lead singer of Big Star was Alex Chilton (1950-2010), who was a cult rock hero in the 1980s and 1990s, due to Big Star being named as a major influence by bands such as R.E.M. and The Replacements, and championed by Rolling Stone. Is is possible that Rory’s school was at least partly named in his honour?