Yea, there isn't really any harm in it, but you may not be able to run as well as if you eat something in the morning. Your blood/liver glucose levels are low in the morning and you can burn through it quick which is going to limit how hard/fast you can run.
When I train clients, it never fails that the ones I train in the morning who don't eat (despite what I tell them) get light headed and pale 15 minutes into a tough workout. Eat some simple carbohydrates (banana is great) or something that isn't going to sit in your gut or cause GI distress when you run.
Also, you *may* burn more fat by not eating in the morning, but you probably won't be able to work as hard and, thus, not burn as many calories which is really the bottom line if you're trying to lose weight (not sure if you are). So, I wouldn't recommend not eating in the morning as a way of losing weight if that is why you are beginning to run.