I tried giving him some of his favorite treats and he wouldn't eat them. (He NEVER turns down his treats)
You have a very sick chinchilla on your hands.
What do his poops look like? Normal -oval moist, but firm OR Dirrhea - soft, mushy, sticking to everything, OR small, hard and dry and not as many of them as usual ...
Is he still drinking the normal amount of water? These two questions and their answers are VERY important.
You have reason to be concerned and I do suggest he sees an exotic pet vet, that is familiar with chinchillas, as soon as possible. Chinchillas have a tendency to hide their illness ... more times than not, by the time you know something is wrong, it could be to late to do much about it.
Loosing fur around the paws could be caused by many things ... a fungus, nerves, ringworm, to many dust baths/dry skin, etc.
A wet eye could mean many things ... some of which can be fixed with medication, some of which are not easily fixed ... but he does need to be seen by an exotic pet vet that is familiar with chinchillas to find out what is wrong and if it can be fixed. Virus, infections, bacteria, a small scratch on the eye or around it and/or tooth problems ... just to mention a few ... it could be any one of these. None are good, but some are much worse than others.
Not eating good could be due to not feeling good or could be due to being sick or due to a bowel blockage ... you need to find out for sure and do so a.s.a.p. Regardless of the reason, it needs to be corrected quickly. A chinchilla that is not eating means it's digestive system is not working properly, or it may be blocked, or he is sick, or the digestive system is shutting down ... not a good thing. When the digestive system shuts down, a chinchilla can easily/quickly die.
He could have something as simple as something stuck between his teeth, making his gums to sore to eat ... Or ... a cracked or chipped tooth, same effect ... OR ... malocclusion (hopefully not). A chinchilla usually eats, unless he is in pain or sick.
If you can not get to a vet today, I suggest you give your chin some yogurt or acidophilous, mixed with some ground up hay and/or pellets. If you have a food processor or a blender, either of these can be used to grind up the hay and/or pellets.
Using the yogurt and/or acidophilous mixed with the ground pellets will help replace the flora in his digestive system (hopefully getting it started again or keeping it from shutting down completely) and help him hold on a bit longer, maybe until a vet can see him tomorrow. Acidophilous has to be refrigerated after opening. Make the mix into tiny little footballs about the size of a raisin and give him 1 or 2 at a time ... keep the others refrigerated in an airtight jar, until you are ready to give them to him. If he refuses these, try giving him the yogurt with a tiny bit of ground hay, using a glass eye dropper ... one drop at a time, if necessary.
Please keep us posted.
Jo Ann
P.S. If the digestive system is blocked ... if his poops are small and hard and very few in number ... this is the only time you will see me suggest using any kind of a nut ... give him one or two almonds, and plenty of water ... even if you have to feed the water to him by using an eyedropper.