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We present a high-resolution spectrum of the diffuse X-ray background from 0.1 to 1 keV for a ∼1 sr region of the sky centered at l = 90°, b = +60° using a 36 pixel array of microcalorimeters flown on a sounding rocket. With an energy resolution of 11 eV FWHM below 1 keV, the spectrum's observed line ratios help separate charge exchange contributions originating within the heliosphere from thermal emission of hot gas in the interstellar medium. The X-ray sensitivity below 1 keV was reduced by about a factor of four from contamination that occurred early in the flight, limiting the significance of the results. The observed centroid of helium-like O VII is 568+2– 3 eV at 90% confidence. Since the centroid expected for thermal emission is 568.4 eV and for charge exchange is 564.2 eV, thermal emission appears to dominate for this line complex. The dominance of thermal emission is consistent with much of the high-latitude O VII emission originating in 2-3 × 106 K gas in the Galactic halo. On the other hand, the observed ratio of C VI Lyγ to Lyα is 0.3 ± 0.2. The expected ratios are 0.04 for thermal emission and 0.24 for charge exchange, indicating that charge exchange must contribute strongly to this line and therefore potentially to the rest of the ROSAT R12 band usually associated with 106 K emission from the Local Hot Bubble. The limited statistics of this experiment and systematic uncertainties due to the contamination require only >32% thermal emission for O VII and >20% from charge exchange for C VI at the 90% confidence level. An experimental gold coating on the silicon substrate of the array greatly reduced extraneous signals induced on nearby pixels from cosmic rays passing through the substrate, reducing the triggered event rate by a factor of 15 from a previous flight of the instrument. [ABSTRACT FROM AUTHOR]