This is a disputed piece, and frankly, we do not have enough information to decide the debate.
Option 1: The Reiss "Nanette" (engagement dress) in black. This would be a strong contender. Kate has been known to buy the same piece in multiple colors. Her Amanda Wakeley "Sculpted-Felt" sheath and the Temperley Honeycomb jumper are just two examples. The slant of the skirt, particularly in the Christmas photo, suggests the Nanette, however, Reiss has confirmed the dress was never produced in black.
Option 2: Temperley "Simonette". This frock has the requisite front detail, but seems to have too much layering to match the two coats the Duchess has paired with this dress.
It has been suggested that it is Issa, but the dress that has been highlighted was produced after her engagement, and it seems unlikely Kate has purchased Issa since she announced she would be joining the Royal Family.
Lastly, it could be an entirely different dress altogether.
It's up for debate. Detailed discussion can be found on sterling Kate blog, What Kate Wore.