The song isn't advertising Jekyll it's for Heroes and is originally by Skeeter Davis - her version is a bit country but see this excerpt from Wiki :
The song has been covered by a number of artists on albums, including The Carpenters, Loretta Lynn, Herman's Hermits, John Cougar Mellencamp, Johnny Mathis, Julie London, Eddy Arnold, Dottie West, Nancy Sinatra, Sonia Evans, Twiggy, Claudine Longet, Agnetha F�ltskog (of ABBA fame), Patti Page, Anne Murray, Nina Gordon, Vonda Shepard, Expos�, The Vanguards, and others, but Davis' remains the definitive performance.
I think it's Nancy Sinatras version - been to itunes and you can hear a clip - sounds like its her.
hope this helps