Claire Danes and new British boyfriend Hugh Dancy head to her NYC apartment after shopping for Italian food at a nearby supermarket. The acting couple, who wore matching outfits of jeans, black jackets, and scarves, laughed and walked hand in hand.

Claire, 28, and Hugh, 31, met on the set of Evening, out June 29. Hugh has said, “I am, however, seeing Claire. And today I live in New York, downtown, which I love.”

In addition to starring in a high-profile Broadway play (Journey’s End), Hugh has four films coming out this year (Evening, Savage Grace, The Jane Austen Book Club and Brontë).

Claire’s next movie The Flock co-stars Richard Gere and is set for a May 11 release. The Flock tells the story of a hyper-vigilant federal agent (Gere) who, while training his young female replacement (Danes), must track down a missing girl whom he is convinced is connected to a paroled sex offender he’s investigating.

Claire also attended the Conde Nast Travelers Annual Hot List Issue Party at NYC’s The Bowery Hotel on Thursday night.

20+ pictures inside of Claire and Hugh…

British-born actor Hugh Dancy arrives at the curtain call for the opening night of the Broadway play Journey’s End at the Belasco Theatre on Thursday night in New York City.

His rumored girlfriend Claire Danes arrived with him to the opening night party. Journey’s End is an adaptation of the 1928 drama set in the French trenches during the World War I.

Hugh, 31, also has a film coming out called Beyond The Gates, which tells the story of an exhausted Catholic priest and a young idealistic English teacher (Dancy) who find themselves caught in the 1994 Rwandan genocide. They must choose whether to stay with the thousands of Tutsis about to be massacred or to flee for safety.

Beyond the Gates opens in limited theaters nationwide on March 9.

For more pictures of Hugh and Claire, CLICK HERE!

I cannot believe Hugh is 31, he looks 20!