Generally the answer is no, however if this person is having you over at their house you may feel inclined to get them a present. The last thing you want to do is look like a fool on the first day of the year which is supposed to be for new beginnings (great start to the year, huh?). Ask around and see if other people you know are giving this person a present as well.
If your friends are getting gifts for this person as well here are some ideas: A bottle of wine Chocolate
If someone was hosting a party I would definitely bring a bottle of wine or another nice hostess gift. Sometimes it seems like the same person ends up giving most of the parties and I think it is nice to always thank them with a small show of gratitude.