Transient x-ray radiography using laser-plasma emission is a powerful tool for diagnosing a large variety of high-energy-density phenomena. Traditional area- and point-backlighting techniques used at inertial confinement fusion facilities such as Nova and Omega cannot be extended efficiently to the future 100-times-larger National Ignition Facility. We have developed an x-ray backlighting technique that uses a backlit pinhole as a source for point-projection radiography. This method incorporates the principal advantages of point projection over traditional area backlighting in that it requires far less backlighter energy and produces data that are free from residual backlighter plasma structure. Moreover, the use of pinholes overcomes the usual disadvantages of point projection from pin targets, namely, degradation of spatial resolution and cooling due to plasma expansion.