An intense femtosecond Ti-sapphire laser pulse was focused into water, leading to self-focusing. Apart from generating a white light (supercontinuum), the intense laser field in the self-focusing regions of the laser pulse dissociated the water molecules, giving rise to hydrogen and oxygen gas as well as hydrogen peroxide. Our analysis shows that the formation of free radicals O, H, and OH preceded the formation of the stable products of H(2), O(2), and H(2)O(2). Because O radicals and H(2)O(2) are strong oxydizing agents, one can take advantage of this phenomenon to design a laser scheme for sterilization in medical and biological applications.