Ignition of exothermic chemical reactions in small volumes is considered as difficult or impossible due to the large surface-to-volume ratio. Here observation of the spontaneous reaction is reported between hydrogen and oxygen in bubbles whose diameter is smaller than a threshold value around 150 nm. The effect is attributed to high Laplace pressure and to fast dynamics in nanobubbles and is the first indication on combustion in the nanoscale. In this study the bubbles were produced by water electrolysis using successive generation of H(2) and O(2) above the same electrode with short voltage pulses in the microsecond range. The process was observed in a microsystem at current densities >1000 A/cm(2) and relative supersaturations >1000.