I hate to admit it, but I didn’t know any Jewish people when I lived in California. Since moving to NY last year, I’ve made one good friend who was raised Jewish, but isn’t religious (nor am I). I know she’s getting me a Christmas present; should I just give her something then? Wednesday? Some other day of Hanukkah?
Oh, and I said Wednesday thinking that was the first day, but apparently it was tonight. Whoops!
That’s really thoughtful of you. I can’t speak for every Jew but I’ve gotten used to giving and recieving gifts at Christmas-time since that’s when most of my friends do – I’m not at all offended to get gifts then. However, tonight, my roommate, who isn’t Jewish, gave me a gift for Hanukah which made me really happy 
So, I say, go for it if it wouldn’t be too difficult to get a gift ready in the next eight days.
Speaking as the one and only Jewish person in my group of friends, I like Hanukauh presents! And Christmas presents. I do buy presents for my close friends for Christmas, and many of my friends also buy me gifts, but seem shy about the “correctness” of it and tend to be unsure about when to give. Like stucco, I can’t speak for all, but I don’t know of anyone who’d be mad because they got a present on the wrong day.
Anyhow - giving is giving. It’s always very kind and appreciated, by anyone. You giving her a Hanukkah present is no less strange than her giving you a Christmas present.
Agreed that gifts are always enjoyed an appreciated.
That said, be aware that gift-giving is not an integral part of Hannukah (it is NOT the “Jewish Christmas”) But its absolutely fine to give and receive gifts. Give 'em for Hannukah, Christmas, or as I prefer “Festive Commercial Gift-Giving Season.” Who doesn’t like presents?
Or you can give the traditional “Chanuka Gelt” (thats money).
I thought gelt was the little chocolate coins. 
“gelt” means gold. In Yiddish, it meant money, usually coins. It is also the name for the chocolate coins sold around Chanukah. I always find it strange when Chanukah “gelt” comes in silver wrappers. 