I used these catch basins with the matching hose to drain water from around my shops. You might look at a trench drain as well.
JT
I like JT's catch basin idea, not much digging needed, you could bury it in the run at the lowest point. You can then cover it with landscape fabric and whatever bedding you have in the run and the chickens can walk all over it and scratch and dig as normal and not get their toes caught. You could buy one cheap or make your own if you've got a spare bucket or something around.