I'm usually awakened by the sun rising. In the summer months, this means that I'm rousing at around 5:30 or 6 AM. Chicken duty is the first thing I do when I get out of bed: fill up a gallon jug with water and then off to give the chickens water refills and let them out.
In the summer months, if I want to sleep in then it's no big deal. I use an Eglu and I just leave the door to the house open, but lock up the run at night. That keeps predators from getting in at them and means they can get up as early as they want to eat (I keep the food containers filled at all times) and drink water that has been left in the run over night.
The Eglus are inside a larger fenced run, so "letting the chickens out" means opening up the door to the Eglu run so they can wander around the large run during the day.
Now that the weather is getting colder at night, I close the door to the house at night, too. I also empty the water containers at night so nothing freezes. There is no food inside the house, so if I'm not up early to let them out, they get pretty agitated. However, the sun is coming up later and later these days, so I can let them out as late as 7 AM.
With my work schedule, I usually have to let them out no later than 6:30 AM, anyway. The other day I had to be at work at 7 AM, so I was letting them out at 5 AM, a full 2 hours before sunrise. Not ideal since there still could be a racoon or such roaming around at that time, but there wasn't much control I had over the situation.