We report sub-arcsecond resolution X-ray imaging spectroscopy of the low luminosity active galactic nucleus of NGC 4258 and its immediate surroundings with the Chandra X-ray Observatory . NGC 4258 was observed four times , with the first two observations separated by one month , followed over a year later by two consecutive observations . The spectrum of the nucleus is well described by a heavily absorbed ( N _ { H } \simeq 7 \times 10 ^ { 22 } \hbox { $ { \thinspace cm } ^ { -2 } $ } , which did not change ) , hard X-ray power law of variable luminosity , plus a constant , thermal soft X-ray component . We do not detect an iron K \alpha emission line with the upper limit to the equivalent width of a narrow , neutral iron line ranging between 94 and 887 eV ( 90 % confidence ) for the different observations . During the second observation on 2000-04-17 , two narrow absorption features are seen with > 99.5 % confidence at \simeq 6.4 keV and \simeq 6.9 keV , which we identify as resonant absorption lines of Fe XVIII – Fe XIX K \alpha and Fe XXVI K \alpha , respectively . In addition , the 6.9 keV absorption line is probably variable on a timescale of \sim 6000 sec . The absorption lines are analyzed through a curve of growth analysis , which allows the relationship between ionic column and kinematic temperature or velocity dispersion to be obtained for the observed equivalent widths . We discuss the properties of the absorbing gas for both photo and collisionally ionized models . Given that the maser disk is viewed at an inclination i = 82 ^ { \circ } , the gas responsible for the 6.9 keV absorption line may be in an inner disk , a disk-wind boundary layer or be thermal gas entrained at the base of the jet . The gas which gives rise to the photoelectric absorption may be the same as that which causes the 6.4 keV Fe K \alpha absorption provided that the gas has a bulk velocity dispersion of a few thousand km s ^ { -1 } . This is the first detection of iron X-ray absorption lines in an extragalactic source with a nearly edge-on accretion disk , and this phenomenon is likely to be related to similar X-ray absorption lines in Galactic X-ray binaries with nearly edge-on accretion disks .