We present a high-resolution Chandra X-ray observation of PSR B0540-69, the Crab-like 50 ms pulsar in the Large Magellanic Cloud. We use phase-resolved imaging to decompose the extended X-ray emission, as expected of a synchrotron nebula, from the pointlike emission of the pulsar. The image of the pulsed X-ray emission shows a well-defined point-spread function of the observation, while the resolved nebula has a morphology and size remarkably similar to the Crab nebula, including evidence for a jetlike feature from PSR B0540-69. The patchy outer shell, which most likely represents the expanding blast wave of the supernova, is reminiscent of that seen in radio. Based on morphology, size, and energetics, there can be little doubt that SNR B0540-69 is an analogous system to the Crab but located in our neighboring galaxy.