Originally recorded by The Rivileers (1954).
Hit version by Kathy Young & The Innocents (US #3/R&B #6 1960).
From the wiki: “The Rivileers were an R&B quintet who recorded for the Sol Rabinowitz’s New York City-based Baton Record label. ‘A Thousand Stars’ was the label’s first release. (The label’s most enduring hit is arguably ‘Got My Mo-Jo Working‘, first recorded by singer Ann Cole in 1957.)