Mary Lou (Jessie-Ling) by Ronnie Hawkins and The Hawks
Label credit aside, this was co-written and first recorded in 1955 by Young Jessie (aka Obie Jessie).
THE 1959 HITS ARCHIVE - here in one place, a good-quality library of original-release-version best-sellers and songs that made an impact that were either released or enjoyed a major chunk of their popularity within the calendar year 1959 (some were recorded in 1958).