Anytime you see fur around the mouth or chin of your rabbit that is staying wet it can mean a bacterial infection that turns the fur green, or and a tooth problem causing drooling.
One minor problem causing green chin is if a rabbit is overweight or has a large dewlap. A dewlap is a roll of skin like a double chin, in unspayed females, females that are spayed later in age or overweight rabbits. When a rabbit drinks out of a water bowl the fur can constantly dip into the bowl wetting the dewlap and causing green chin.
Tooth problems can be malocclusion which is where the teeth don’t line up properly and overgrow. Another problem is where a molar tooth grows a molar spur which can poke into the cheek or tongue. A missing tooth can cause the tooth below or above to overgrow.
All of these can hinder or stop your rabbit from being able to eat. A molar spur can grow into the tongue or cheek causing pain. An overgrown tooth can grow into the roof of the mouth or out of the mouth and can keep growing. In all cases, a trip to the vet is needed.
Teeth may be trimmed, which will be ongoing or they can be removed. A head X-ray is a good idea so your vet can see all the teeth. It is very important to go to an exotic vet that is knowledgeable in rabbits and rabbits’ teeth, especially for a tooth removal.