The Wikipedia entry notes that bodies were built by the Karmann firm, but the design was by Ghia's Luigi Segre.
But the matter of styling wasn't that simple. During the early 1950s, Chrysler Corporation contracted with Ghia to build customized show cars designed by Virgil Exner and his staff. It happened that the Karmann-Ghia used a number of styling cues from the Chrysler D'Elegance show car of 1952-53. (It was built in 1952 and displayed at the Paris auto show, but didn't debut in the USA until 1953 -- so both years have been cited for it.)
Regardless, the Karmann-Ghia is widely considered an outstanding design.