Did some extensive google research here - it seems quite a complex reaction but can be summerized as...
Heat causes the proteins in the egg to aggregrate (mass together into large complexes) this process is known as coagulation.
This results in denaturation of the proteins - changes to the molecules that alter the properties of the proteins.
The molecules in the proteins start to become less soluble in water and precipitate hence the colour change.
Good answers but just to add that, in many people's opinion, it is not a chemical reaction, ie the protein molecules are rearranged but not chemically changed.