Progeria is a very rare disease which causes children to undergo symptoms extremely similar to rapid aging, and generally dying before the age of 20. Recent results suggest that a fairly cheap drug may help reduce the aging systems, and it is possible it may have similar effects on normal humans. Lay summary by BBC and actual article
On a related note, in a strain of mice which age unusually quickly, there's been success delaying many symptoms of aging by removing senescent cells. Here is the relevant article in Nature.