We present high angular resolution Submillimeter Array observations ofthe outbursting Jupiter family comet 17P/Holmes on 2007 October 26-29, achieving a spatial resolution of 2.5, or ~3000 km at the comet distance. The observations resulted in detections of the rotational lines CO 3-2, HCN 4-3, H$^{13}$CN 4-3, CS 7-6, H$_2$CO 3$_{1,2}$-2$_{1,1}$, H$_2$S 2$_{2,0}$-2$_{1,1}$, and multiple CH$_3$OH lines, along with the associated dust continuum at 221 and 349 GHz. The continuum has a spectral index of 2.7$pm$0.3, slightly steeper than blackbody emission from large dust particles. From the imaging data, we identify two components in the molecular emission. One component is characterized by a relatively broad line width (~1 km s$^{-1}$ FWHM) exhibiting a symmetric outgassing pattern with respect to the nucleus position. The second component has a narrower line width (<0.5 km s$^{-1}$ FWHM) with the line center red-shifted by 0.1-0.2 km s$^{-1}$ (cometocentric frame), and shows a velocity shift across the nucleus position with the position angle gradually changing from 66 to 30 degrees within the four days of observations. We determine distinctly different CO/HCN ratios for each of the components. For the broad-line component we find CO/HCN <7, while in the narrow-line component, CO/HCN = 40$pm$5. We hypothesize that the narrow-line component originates from the ice grain halo found in near-nucleus photometry, believed to be created by sublimating recently released ice grains around the nucleus during the outburst. In this interpretation, the high CO/HCN ratio of this component reflects the more pristine volatile composition of nucleus material released in the outburst.