Final answer:
The Helium-3 nucleus is held together by the strong nuclear force, which overcomes electrostatic repulsion between protons and binds nucleons inside the nucleus.
Step-by-step explanation:
The main force that holds a Helium-3 nucleus, which consists of two protons and one neutron, together is the strong nuclear force. This is one of the four fundamental forces in physics, and within the nucleus, it overcomes the electrostatic repulsion between the positively charged protons, holding them tightly together alongside the neutrons. At distances smaller than 10-15 meters, the strong nuclear force is substantially more powerful than the repulsion caused by the electromagnetic force, effectively binding the nucleons. Outside the nucleus, the strong nuclear force is practically non-existent.