The Midnight Cellar Test

A vintner has 1,000 sealed barrels. Exactly one contains a fatal poison; the rest are harmless. Anyone who tastes the poisoned liquid dies exactly 24 hours later, with no earlier symptoms. You have a group of tasters available now, and each taster may sample from any number of barrels. Samples may also be combined, so a taster can drink one mixture containing drops from many barrels. All tasting must happen at the same time, and after 24 hours you must identify the poisoned barrel with certainty solely from which tasters are alive or dead. What is the smallest number of tasters required?