Question:
My son is licking his hands and chewing on objects. What can I do about that?

My Opinion:
Regression

My #3 son licks his hands and mouths objects when he eats a "bad food", it is like regression to the baby/oral stage for him. So when I notice that he is becoming oral, I look for a food which he is eating that he has not eaten in a while, or maybe an infraction. You can also consider digestive enzymes from Houston Nutraceuticals or Kirkman Labs.

Yeast overgrowth

My #3 will also lick and mouth things if he has a yeast overgrowth issue. For information on how to address that, see here:
http://www.danasview.net/yeast.htm

Mineral Deficiency

Many parents have discovered that their children stop chewing on objects when they add a zinc supplement to the diet.

Smell

Your hands are involved in pretty much all of your daily activities, and they smell like it. Also, if someone is cooking food in another room, the odors (which are really small bits of food floating around in the air) also get on your hands. Or if you are coloring, playing with the dog or in the dirt, etc, your hands will smell like that stuff too. Does your child like to smell things? For example, a new box of crayons just opened, or a brand new book opened for the first time? The very first thing I do with new crayons, books, etc, is stick my nose in them. Also, if your child is extra-sensitive to gluten and casein, he can get a buzz simply by smelling his hands if they have particles on them from floating odors.

Taste

Smell works in very nicely with taste. If you can't smell something, you can't taste it, which is why nothing tastes like much when you are sick. So if your child smells something on his hands that is nice, he will probably try to lick his hands also. This will contribute to any buzz he may have experienced from the smell, which will encourage that behavior for quite a while, even if there are no more particles on his hands, because he will be hoping at some point to get that buzz again, and will keep trying until he realizes that it was a one-time thing.

Also taste can be for a vitamin/mineral deficiency. A few people here mentioned salt. Salt is very addictive to many kids. I can eat salted sunflower seeds in the shell, sucking all the salt out of them before cracking and eating them, until my tongue is all shriveled and cracked. This also results, obviously, in excess fluid intake. There are other vitamin/mineral deficiencies that can be helped by eating dirt or whatever, like for example iron deficiency/anemia, kids with anemia will generally eat dirt. You can check into that also for your child. But then again, some things just plain taste good. When I was a child, I ate paste straight from the jar. You can check to see what your child may be getting on his hands that he is enjoying for the taste.

Someone here also mentioned licking glass and other objects. They also have a taste which can be their own taste in themselves, or particles of food or toothpaste or cut grass or whatever, that have found their way to the glass.

Touch

Licking your hands comes with a lot of sensory issues. Primary is that your tongue does not get to do too many different things, basically just talking and eating. Are you doing some tongue exercises for speech therapy? Or because of a drooling problem? This will make your child more aware of his tongue and what it can do and how it can feel. Also, licking is a warm feeling, which is then immediately followed by a cold feeling as the moisture evaporates. Plus licking is wet, which dries. All these concepts, especially if also being learned in ABA or other therapy, will be interesting to the child. Plus if this diet is helping your child, he will be more sensitive to this type of feeling, because the drug-like effect of the food is wearing off, and he may have heightened feeling in this tongue or hands, and the rest of his body too.

Licking glass and other objects has similar ideas. Smooth surface, or rough, or hard, or dry, or whatever. Very different feeling than when you touch it with your hands. Your child may simply be exploring how things feel with his tongue, especially if learning these concepts in therapies.

Other Issues

One thing to keep watch for, occasionally autistic kids, especially ones with sensory issues, do have self-injury behaviors (sibs) and one of the primary ones is hand biting. So if your child is licking his hands and liking it, he may progress to biting to see what other sorts of sensory issues he has. While I do not see that licking is necessarily a bad thing, other than it makes other kids and adults stare at him and is not too acceptable for social situations, plus it is not very clean and makes the child susceptible to ingesting non-food things and germs, it seems to me to be relatively harmless as something you might want to discourage, ignore, or redirect, but don't be too extremely upset or insistent about eliminating it too quickly. If you try to eliminate a stim before the child is ready, he will just discover a new stim to release his need, which may result in him having a new stim that is even worse than the current hand-licking stim, such as head banging or something else. Discouraging, ignoring, redirecting, encouraging a more appropriate activity, giving him something else to do with his hands, along with checking for food and environmental issues, all these things will allow the child to move away from the stim at his own pace, with less risk that the elimination will result in replacement with a new and less-desirable stim.