If you live in a city where there is ample street lighting, you could possibly run at anytime of night (or morning) without a problem.
Or, if you time your run correctly, you could also catch the civil twilight, which refers to the moments right before sunrise. This is a window of time where sunlight is illuminating the sky but the sun hasn’t yet risen. Rule of thumb is that this period of time is about a thirty minute window.
For those of us living in smaller municipalities, on the outskirts of cities, or who don’t want to pay attention to timing the civil twilight, it is almost certain you’ll need a headlamp if you’re running in the dark. This becomes even more true if you were planning to run trails in the early morning.
We have a post specifically dedicated to the best headlamps for trail running. Any of those would work perfectly for lighting your way in the pre-dawn hours.