There are other possibilities besides malo that are treatable. I am suggesting an exam because you now have three symptoms that can mean tooth problems. 1. You suspect the animal is underweight. 2. It is suddenly fur chewing. 3. Someone (presumably, but I would ask questions about how bad it is) with experience with chinchillas is saying he is not eating enough hay.
They may also be unrelated and might not mean anything. It might be time to get tooth problems ruled out with an exam to prevent a potential problem from progressing. Of course I have had a bad experience first hand so maybe I am biased towards pushing for this when I shouldn't be. A dental exam carries risk because of the anesthesia so you are better off if you can avoid it.
If he really is underweight and has gone off his hay this is a strong sign that something is wrong somewhere and probably in the back teeth. These are both "IFs" which means they should be verified. Maybe you should get him examined by someone that can at least tell you if he is at the right weight and may be able to explain what is going on without a dental exam. Knowing a healthy weight for your chinchilla is a critical first step. An experienced veterinarian can tell you a lot just by looking and feeling.
If he's healthy you can wait and see and see if there is a decline in weight before you consider the dental exam. If there is a decline that approaches 20% of his current healthy weight and his activity level and environment is constant (or if he goes off his food altogether like mine did) then you'll know you need to get a dental exam and try to get a diagnosis. If he is at a currently unhealthy weight and looses 20% that could be very dangerous. In my case I got a diagnosis and didn't get the tooth exam until I knew it was needed, had a very clear target weight to watch for, and didn't wait until he was dangerously underweight so he survived the anesthesia just fine.
I am certainly not a veterinarian and certainly do not even pretend to know what's going on with your pet. With the stress he's going through now I expect he will loose some weight at the boarding place and reach a new baseline low weight. You will likely see a steep increase in his appetite and weight when he gets home. Perhaps stress in his environment is causing him to favor hay over pellets for some reason and it may be temporary. Ultimately I recommend getting a regular exam (without anesthesia) by a trustworthy vet and go from there because of my own experience.
I hope others will comment.