  We report observations with the Chandra X-ray Observatory of the single,
cool, magnetic white dwarf GD 356. For consistent comparison with other X-ray
observations of single white dwarfs, we also re-analyzed archival ROSAT data
for GD 356 (GJ 1205), G 99-47 (GR 290 = V1201 Ori), GD 90, G 195-19 (EG250 = GJ
339.1), and WD 2316+123 and archival Chandra data for LHS 1038 (GJ 1004) and GD
358 (V777 Her). Our Chandra observation detected no X rays from GD 356, setting
the most restrictive upper limit to the X-ray luminosity from any cool white
dwarf -- L_{X} < 6.0 x 10^{25} ergs/s, at 99.7% confidence, for a 1-keV
thermal-bremsstrahlung spectrum. The corresponding limit to the electron
density is n_{0} < 4.4 x 10^{11} cm^{-3}. Our re-analysis of the archival data
confirmed the non-detections reported by the original investigators. We discuss
the implications of our and prior observations on models for coronal emission
from white dwarfs. For magnetic white dwarfs, we emphasize the more stringent
constraints imposed by cyclotron radiation. In addition, we describe (in an
appendix) a statistical methodology for detecting a source and for constraining
the strength of a source, which applies even when the number of source or
background events is small.
