Better would be something like: "In the last one thousand years" "For the last millennium" (millennium = 1000 years) I'm sure there are more elegant possibilities and it will depend a little on the context. (ie: what is it about?).

I have to add: Martin's answers show that something happened for that entire time (from that time to the present). ex "The tribe has hunted here for a thousand years." You can also say something happened at that time. ex "The tribe hunted here a thousand years ago." Instead of hunting for those thousand years, the tribe only hunted there a thousand years ago -- it is not continuous. Since one thousand years ago can be used as cause and effect (e.g. Since the tribe hunted a thousand years ago, we found arrow heads where they hunted.) or as a continuous action, like Martin said (e.g. The tribe has hunted here since a thousand years ago.)

It's fine.