The correct answer is option 3: Potential energy.

Potential energy refers to the energy that is stored within a system and could be released under certain conditions. In the case of the links between atoms in a substance, potential energy is stored in the form of chemical bonds.

Chemical energy, which is mentioned in option 2, is closely related to potential energy. It refers to the energy that is stored in the bonds between atoms within molecules. When these bonds are broken or formed, energy is either released or absorbed.

Nuclear energy, mentioned in option 1, is the energy that is released during nuclear reactions, such as in nuclear power plants or nuclear weapons. It is not directly related to the links between atoms in a substance.

Thermal energy, mentioned in option 4, refers to the energy associated with the temperature of a substance. It is a form of kinetic energy that arises due to the movement of atoms and molecules. It is not specifically stored in the links between atoms.

Therefore, the correct answer is option 3: Potential energy.