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An observation of Mrk 478 using the Chandra Low Energy Transmission GratingSpectrometer is presented. The source exhibited 30-40% flux variations ontimescales of order 10000 s together with a slow decline in the spectralsoftness over the full 80 ks observation. The 0.15--3.0 keV spectrum is wellfitted by a single power law with photon index of Gamma = 2.91 +/- 0.03.Combined with high energy data from BeppoSAX, the spectrum from 0.15 to 10 keVis well fit as the sum of two power laws with Gamma = 3.03 +/- 0.04, whichdominates below 2 keV and 1.4 +/- 0.2, which dominates above 2 keV (quoting 90%confidence uncertainties). No significant emission or absorption features aredetected in the high resolution spectrum, supporting our previous findingsusing the Extreme Ultraviolet Explorer but contradicting the claims of emissionlines by Hwang & Bowyer (1997). There is no evidence of a warm absorber, asfound in the high resolution spectra of many Sy 1 galaxies including othersclassified as narrow line Sy 1 galaxies such as Mrk 478. We suggest that theX-ray continuum may result from Comptonization of disk thermal emission in ahot corona through a range of optical depths.