A compact steam reformer produces hydrogen to power a fuel cell, such as can be used in a vehicle. The steam reformer includes a first channel, at least partly coated with a steam reforming catalyst, and a second channel, at least partly coated with a combustion catalyst, the channels being in thermal contact with each other. Heat from the combustion is used in the steam reforming reaction. In another embodiment, the gas streams feeding the reforming and combustion channels pass through a valve which reverses the gas streams periodically. The combustion channel becomes the reforming channel, and vice versa, so that carbon deposits in the former reforming channel are burned off. This arrangement enables the reforming reaction to continue indefinitely at peak efficiency.