High-contrast coronagraphic imaging of the immediate surrounding of stars requires exquisite control of low-order wave-front aberrations, such as tip-tilt (pointing) and focus. We propose an accurate, efficient, and easy to implement technique to measure such aberrations in coronagraphs which use a focal plane mask to block starlight. The coronagraphic low-order wave-front sensor (CLOWFS) produces a defocused image of a reflective focal plane ring to measure low-order aberrations. Even for small levels of wave-front aberration, the proposed scheme produces large intensity signals which can easily be measured, and therefore does not require highly accurate calibration of either the detector or optical elements. The CLOWFS achieves nearly optimal sensitivity and is immune from noncommon path errors. This technique is especially well suited for high-performance low inner working angle coronagraphs. On phase-induced amplitude apodization (PIAA)-type coronagraphs, it can unambiguously recover aberrations which originate from either side of the beam shaping introduced by the PIAA optics. We show that the proposed CLOWFS can measure sub-milliarcsecond telescope pointing errors several orders of magnitude faster than would be possible in the coronagraphic science focal plane alone, and can also accurately calibrate residual coronagraphic leaks due to residual low-order aberrations. We have demonstrated 10-3l/D pointing stability in a laboratory demonstration of the CLOWFS on a PIAA-type coronagraph.