As some have said already, chickens don't eat at night. There are a few things you would need to take into consideration though.
Will you be locking them in the coop at night? If so, you would want to probably keep some food in the coop for if they wake up before you let them out. Otherwise if they can move freely between the run and coop at all times you don't neccesarily need food in the coop.
Is the run, or part of the run sheltered from the weather? If the run is sheltered and your chickens have access to it, I find my chickens prefer to be outside during the day and don't go into the coop until they want to roost, having food on the outside only is fine. But if you have extreme weather and there are days that your chickens prefer to stay inside, you would want to keep food and water inside too.
How often do you want to clean out the coop? If your chickens spend a lot of time in the coop you will probably need to clean it a lot more often, where if they spend most of their time out in the run, I find the coop needs very little cleaning.
So it depends on the size and style of your coop and run and also on your personal preference. If you give us more detail about your coop we can give you more specific tips. But in the end you will probably find that you will need to make adjustments as you go along until you find what works for you.