I was once reading the ingredients on a pack of Bissli (with a Pesach hashgacha) and saw that it contained yeast. How can this be?
Yeast is not Chametz.
Chametz is defined as the five grains rising.
Yeast, on the other hand, is made from potato:
In general, yeasts are grown in the laboratory on solid growth media or in liquid broths. Common media used for the cultivation of yeasts include potato dextrose agar or potato dextrose broth, Wallerstein Laboratories nutrient agar, yeast peptone dextrose agar, and yeast mould agar or broth.
Yeast are single celled microorganisms that are classified as Fungi and can be found on everything. There are many sources of yeast which do not come in contact with chometz and therefore are not a concern for pesach such as grapes and other fruits and vegetables.
Leaven is a chemical interaction between any of the 5 grains wheat, spelt, oats, barley, or rye and yeast. (And, technically, what we today call oats isn't the original oat, not "shibolet se-orah" as it was back then. It actually doesn't ferment like the other 4, so we likely lost a species along the way an substituted.) Yeast alone is not leaven, as wheat and water baked quickly enough is not leaven, as the yeast in the air hasn't enough time to leaven it, and no yeast is otherwise added.