Well, it is normal for them to "chase" deer but to actually take them down usually intells other circumstances such as deep snow that is crusted over, or a pack of coyotes involved instead of a single, or a wounded deer that the coyote sinces is week, etc. It's a fact that coyotes take down deer, but for one coyote to take down one full grown healthy deer on dry ground, it's not likely! Coyotes prefer easy meals, so they won't expend much energy "chasing" something that they probably can't handle!
The fawning season is when the coyotes will make a dent in the deer population!