  We report on the results of 18 observations of the core, or peak, of the Fe K
emission line at $\sim 6.4$ keV in 15 Seyfert I galaxies using the {\it
Chandra} High Energy Grating (HEG). These data afford the highest precision
measurements of the peak energy of the Fe K 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 17 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 15 sources the two-parameter, 99% confidence errors on the line peak
energy do not exclude fluorescent $K\alpha$ line emission from Fe {\sc i},
although two sources (Mkn 509 and 3C 120) stand out as very likely being
dominated by $K\alpha$ emission from Fe {\sc xvii} or so. We were able to
measure the line core width in 14 data sets and obtained a weighted mean of
2380 +/- 760 km/s FWHM (excluding the NGC 3783 deep exposure), a little larger
than the instrument resolution. However, there is evidence of underlying broad
line emission in at least 4 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 {\it 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 line.
