We study the liquid-crystalline phase behavior of a concentrated suspension of helical flagella isolated from Salmonella typhimurium. Flagella are prepared with different polymorphic states, some of which have a pronounced helical character while others assume a rodlike shape. We show that the static phase behavior and dynamics of chiral helices are very different when compared to simpler achiral hard rods. With increasing concentration, helical flagella undergo an entropy-driven first order phase transition to a liquid-crystalline state having a novel chiral symmetry.