ON JULY 5, 1996, in a shed near the town of Roslin, Scotland, a remarkable lamb was born. The people who gathered around to observe this lamb's birth were not sheep farmers but scientists who worked at a research center called the Roslin Institute. They named the lamb Dolly.

Dolly looked quite ordinary. She had grayish white wool and weighed fourteen and a half pounds. But in a few months, she would become the world's most famous sheep. What made Dolly remarkable was that she was a clone, the first of her kind. She had not been made in the usual way—by the coming together of a male sheep and a female sheep out in the pasture. Her life began in a laboratory.

A clone is an exact genetic copy of a living thing—that is, the genes of the clone are exactly the same as the...