The little girl, who has yet to be given a name, was born at 00:14.
She weighed in at 7lb 13oz. Both she and her mother, Kerry Docherty from Paisley, are reported to be doing well.
Elsewhere in Scotland, a boy was born at Forth Valley Royal Hospital at 03:30. Stacey and Jamie Pryde from Tillicoultry's son Flynn arrived weighing 7lb 9oz.
The first Christmas baby in Scotland is believed to have been born at the Royal Alexandra Hospital in Paisley.