As the human body ages, it loses bone. Individual cells lose something equally vital. Every time one divides, it sheds tiny snippets of DNA known as telomeres, which serve as protective caps on the ends of chromosomes. After perhaps a hundred divisions, a cell's telomeres become so truncated that its chromosomes--site of the cell's genes--begin to fray, rather like shoelaces that have lost their plastic tips. Eventually, such aged cells die--unless, like "immortal" cancer cells, they produce telomerase, an enzyme that protects and even rebuilds telomeres. Scientists have long dreamed of drugs that would inhibit the immortalizing enzyme because, observes M.I.T. biochemist Robert Weinberg, "then maybe cancer cells would run out of telomeres and just poop out." Wishful thinking? Maybe not. In...