One good example for biological based chemical that we normally use is ethanol. C2H5OH.
Ethanol can be produced by a variety of biological sources. The ancient method was to ferment the sap from the plants like coconut and other related trees.
But nowadays ethanol is widely produced by using malt, rice and sugar cane, those ethanol are for drinking as a beverage. But as you might be aware of there is bioethanol which is used as fuel.
Bioethanol is produced mainly by using corn, biological wastes such as rice straw and corn stover.