The element crucial for the formation of strong chemical bonds in organic molecules is carbon. Carbon's unique ability to form four covalent bonds with other atoms allows it to create a diverse array of complex molecules, including fats, proteins, carbohydrates, and nucleic acids. This versatility makes carbon foundational for the structure and function of all biological systems. Its presence in various organic compounds is what distinguishes organics from inorganics, leading to the extensive diversity of life forms we see on Earth.