We have developed a new design for a cryogenically cooled monochromator employing a thin-crystal strategy which is capable of handling the central-cone power of the advanced photon source's undulator A at machine currents up to 300 mA. The key to the proposed design is to machine two opposing narrow channels in a large, indirectly cooled block of Si crystal, leaving a thin, similar to 0.6-mm-thick strip of Si. The thin section absorbs only a fraction of the incident beam power so that the operating temperatures of the crystal are in the range where Si has both a very high thermal conductivity and a very small or slightly negative thermal expansion coefficient. The fact that the crystal is operated in the negative range of thermal expansion means that the crystal surface illuminated by the x-ray beam is always under tension and therefore will not buckle.