A few months ago, as summer was turning to fall, my dog Chester began to shed profusely. He’s a fluffy mutt, part-Australian shepherd (I think), and emits a cloud of hair all the time—but twice a year ...

Got a dog that sheds? Pat Martinek would be happy to take that fur off your hands--or your sofa--and spin it into soft sweater wool known as chiengora. WSJ's Stephanie Simon reports from Golden, Colo.