I'm trying to find a movie made in 85 or86. It is about a boy and girl falling in love while on the run, but I can't remember who is chasing them or why. Sorry this isn't much to go on but I would love to find this movie.

Hmmm... could it be "Fire with Fire" aka "Captive Hearts" (1986)
A young woman from a Catholic school and a young man from a nearby prison camp fall in love and must runaway together to escape the law, the church and their parents.

The Legend of Billie Jean?

Could be The Sure Thing with John Cusack?