Abstract: According to Hund (1927) quantum mechanics forbids the existence of stable optically active (chiral) molecules as they violate the invariance under parity of the Hamiltonian. This paradox has attracted much attention ever since and there is not yet a universally accepted explanation. I will contend that spontaneous symmetry breaking provides a qualitative and quantitative explanation. A second puzzle concerning chiral molecules is homochirality in living matter. This means the almost uniform configuration of aminoacids and  sugars, left handed and  right handed respectively. I will suggest that spontaneous symmetry breaking and symmetry restoring phase transitions in non equilibrium may offer a clue to this problem.