We present a Chandra X-ray observation of G12.82-0.02, a shell-like radio supernova remnant coincident with the TeV gamma-ray source HESS J1813-178. We resolve the X-ray emission from the co-located ASCA source into a point source surrounded by structured diffuse emission that fills the interior of the radio shell. The morphology of the diffuse emission strongly resembles that of a pulsar wind nebula. The spectrum of the compact source is well-characterized by a power-law with index Gamma approx 1.3, typical of young and energetic rotation-powered pulsars. For a distance of 4.5 kpc, consistent with the X-ray absorption and an association with the nearby star formation region W33, the 2-10 keV X-ray luminosities of the putative pulsar and nebula are L(PSR) = 3.2E33 ergs/s and L(PWN) = 1.4E34 ergs/s, respectively. Both the flux ratio of L(PWN)/L(PSR) = 4.3 and the total luminosity of this system predict a pulsar spin-down power of Edot > 1E37 ergs/s, placing it within the ten most energetic young pulsars in the Galaxy. A deep search for radio pulsations using the Parkes telescope sets an upper-limit of approx 0.07 mJy at 1.4 GHz for periods >~ 50 ms. We discuss the energetics of this source, and consider briefly the proximity of bright H2 regions to this and several other HESS sources, which may produce their TeV emission via inverse Compton scattering.