Abstract We report on the results of eighteen observations of the core , or peak , of the Fe K \alpha emission line at \sim 6.4 keV in fifteen Seyfert I galaxies using the Chandra High Energy Grating ( HEG ) . These data afford the highest precision measurements of the peak energy of the Fe K \alpha line , and the highest spectral resolution measurements of the width of the core of the line to date . We were able to measure the peak energy in seventeen data sets , and , excluding a very deep observation of NGC 3783 , we obtained a weighted mean of 6.404 \pm 0.005 keV . In all fifteen sources the two-parameter , 99 % confidence errors on the line peak energy do not exclude fluorescent K \alpha line emission from Fe i , although two sources ( Mkn 509 and 3C 120 ) stand out as very likely being dominated by K \alpha emission from Fe xvii or so . We were able to measure the line core width in fourteen data sets and obtained a weighted mean of 2380 \pm 760 km s ^ { -1 } FWHM ( excluding the NGC 3783 deep exposure ) , a little larger than the instrument resolution ( \sim 1860 km s ^ { -1 } FWHM ) . However , there is evidence of underlying broad line emission in at least four sources . In fact , the width of the peak varies widely from source to source and it may in general have a contribution from the outer parts of an accretion disk and more distant matter . For the disk contribution to also peak at 6.4 keV requires greater line emissivity at hundreds of gravitational radii than has been deduced from previous studies of the Fe K \alpha line . Keywords : accretion disks – galaxies : active – line : profile – X-rays : galaxies Accepted for Publication in the Astrophysical Journal 21 November 2003