The "American Horror Story" star and her man, Sinisa Mackovic, were spotted out Monday in NYC showing PDA and looking really excited about their first child together. They held hands, kissed, laughed and Sinisa even rubbed her belly for good luck ... or possibly because of love and stuff.

The Oscar-nominated actress -- who just wrapped on the upcoming HBO mini-series, "We Are Who We Are" -- is about 5 months into what is, technically, considered a geriatric pregnancy.

For those not in the know, that sounds worse than it is. Doctors slap that label on most expectant moms over 35. Chloe's 45, but that's not nearly as risky as it used to be. Remember, Janet Jackson was 50 when she gave birth for the first time.

Chloe and proud papa-to-be Sinisa -- the director of Karma Art Gallery in NYC -- have been together for more than a year.