My older daughter is the same age as yours (3, almost 4) and I let her hold them, though I ask her to sit. For the older chicks, I let her hold some of them and help me move them back and forth from their brooder to the tote we take them outside in, but they are old enough that if she let go they can fly and she's gotten good at holding them properly now. The ones that are skittish I still do, as she just doesn't have big enough hands to keep them from flapping all over. We waited until the day olds were a couple of days old before anyone handled them too. I will trust her alone for brief periods (like while I run and get mealworms out of the fridge), but I agree with a previous poster that if something were to happen to a chick and I wasn't around she wouldn't know what to do. It also depends on her moods and the time of day, if she's really tired I wouldn't leave her alone with a chick even for a minute because she can be a lot rougher.
My 1 year old never gets to hold the chicks, but I'll hold her hand and pet the babies with her. I'll let her try to pet the older ones on her own (with me right next to her in case she gets too rough) but they can generally take care of themselves.