An observation of Mrk 478 using the Chandra Low Energy Transmission Grating Spectrometer is presented. The source exhibited 30-40% flux variations on timescales of order 10000 s together with a slow decline in the spectral softness over the full 80 ks observation. The 0.15--3.0 keV spectrum is well fitted 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 keV is well fit as the sum of two power laws with Gamma = 3.03 +/- 0.04, which dominates below 2 keV and 1.4 +/- 0.2, which dominates above 2 keV (quoting 90% confidence uncertainties). No significant emission or absorption features are detected in the high resolution spectrum, supporting our previous findings using the Extreme Ultraviolet Explorer but contradicting the claims of emission lines by Hwang & Bowyer (1997). There is no evidence of a warm absorber, as found in the high resolution spectra of many Sy 1 galaxies including others classified as narrow line Sy 1 galaxies such as Mrk 478. We suggest that the X-ray continuum may result from Comptonization of disk thermal emission in a hot corona through a range of optical depths.