Although Ellie Greenwich is justifiably remembered for the classic songs she wrote for groups like the Ronnettes, the Crystals, the Shangri-Las, etc., she also wrote some wonder-making stuff for much lesser-well known groups. The Guardian has a very good obituary, here.
This song was recorded by a group called the "Butterflys". According to a comment on the clip, it got to #51 on the charts in 1964. Ms. Greenwich sings back-up on the track.
I first heard this song when I got the amazing box set "One Kiss Can Lead to Another:Girl Groups Lost and Found". The set, which comes in a cool 'hatbox', take its name from a line in this song, and it's the last song on the 4 CD set.
It makes me very happy to have found this and share it with people who may not have been familiar with it. Thank you to VinylRecords60, and thank you Ellie.