How long have you had your pets? How tame are they?
I suspect what you encountered is fur slip, which is a defense mechanism in chinchillas to make them slippery if a predator attempts to grab one. This is more prevalent in chinchillas that are not tame and are not comfortable with being handled or held.
If just got your pets and they are not well socialized I recommend leaving them in their cage for at least a week if possible and let them get bonded to you before you remove them from the cage to interact with them. This should have a calming effect on them.
If the skin underneath looks irritated or red then you could be faced with an injury or a fungal infection and you should get it checked out. Otherwise instant hair loss on chasing and grabbing a chinchilla is most likely fur slip. I don't consider this to be normal because it indicates your chinchilla may be highly stressed. It does happen on occasion with my pets that are tame but it is rare and usually there is a good explanation for it.