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Chicken feathers are the answer to cleaning up petroleum spills. So say Prof. Alfred Crotti and a business associate, who are confident enough in their discovery that they have organized a company that will manufacture mesh fabric ''pillows'' filled with processed chicken feathers. When the feathers are dropped into an oil spill, Mr. Crotti said, they absorb 28 times their weight in oil while the water falls away. The bags absorb the heaviest oils, work in the roughest waters, and don't sink.