The rate of nuclear fusion from tunneling in very dense metallic hydrogen in the core of Jupiter is calculated to be 10{sup {minus}50} per hydrogen-deuterium pair per second. It is estimated that the width of the fusion barrier for deuterium in palladium or a similar metal must be reduced to, of order, 0.1 A for the fusion rate to be 10{sup {minus}25} per deuterium per second. If this scale is achieved, the ratios of various nuclear reaction rates will be very different for cold versus thermonuclear fusion.