Feather plucking, chewing or over preening is all dangerous behaviors that must be stopped. That seems easier said than done. The first thing is to try to analyze what made the bird start plucking in the first place. It is sometimes easier to change the cause than to change the bird. Sad to say but the faster you catch the problem the better your chances of eliminating it. The first thirty days are critical.
Many factors come into play like diet and how long the behavior has been going on. Do not try to change the problem overnight. Much depends on the type of bird, for some reason different birds are more common pluckers than others. For example: Cockatoos and Grays are more likely to pluck than Amazons or Conures and for no known reason. There are also reasons to believe that feather plucking may be inherited from parents.
If you notice feather plucking or over preening, the bird should first be checked by an Avian Vet. There is a chance the problem is purely physiological. For example there are many illnesses that could cause plucking such as Giardia infections, feather cysts, zinc overdose or even mites, All these problems can usually be cured by your vet. If all those problems are ruled out your bird may also have allergies or have a diet deficiency. Remember that bad behavior in bird's manifest very quickly but do not overreact in front of the bird. Birds are social animals and if they notice this behavior is getting them added attention it may add to your problem.
Another factor could be environmental or diet. Birds need fresh air and high humidity for healthy feathers. If there is a smoker in the house the smoke can sometimes cause over preening which can result in picking. Also, extra dry air can leave skin dry and itchy. A humidifier may be of great help. Also, bathing birds more frequently in winter months keeps their feathers moist.
Diet is also very important. A well balanced diet of pellets (50%), seed (20%), fruit (10%) and vegetables (20%) may help. Furthermore, the best prevention is precaution. Try to keep your bird away from high stress situations. Sometimes children or pets can add stress. Try to make few abrupt changes in your bird's life. Spend a little extra quality time with your bird. Also rotate toys and give many safe chewable items. Indestructible toys are boring and can make birds frustrated. Sometimes natural branches or fun foods can make all the difference. In addition, always remember you are part of their flock and calmer people have calmer birds.