The Will and Grace star announced she had split from Daniel Zelman, her husband of 10 years, last month (Dec11), and almost immediately romance rumours linking her to Chase started circulating.
And Messing took things to the next level on Thursday (26Jan12) by inviting her mum and dad to a special Smash screening in New York City - so they could meet her new man.
According to People.com, the couple talked and laughed over dinner in a booth with Messing's parents at the Metropolitan Museum of Art.
But Smash director Michael Mayer isn't surprised by the blossoming romance, adding, "I don't know where Debra and Will would have met (otherwise). Smash brought them together. And the context of their onscreen relationship, I'm sure that triggered a lot."
Coincidentally, Chase, 41, ended his two-year marriage with wife Stephanie Gibson the same month as Messing (Dec11).
Neither has publicly addressed reports they are dating.