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We present the results of X-ray observations of the broad-line radio galaxy 3C~390.3 obtained with ASCA on 1993 Nov. 16. The 0.5--10 keV spectrum of the source is well described by a power-law plus an emission line, with no evidence for either a hard or a soft excess. The photon index is 1.70$\pm$0.05, and the absorbing column density is $(9\pm 1)\times 10^{20}$ cm$^{-2}$, which is somewhat larger than the neutral hydrogen column density in our Galaxy. The observed 2--10 keV flux is $1.6\times 10^{-11}$ erg~cm$^{-2}$~s$^{-1}$ ($\pm$6\%), which is a factor of 3 lower than the flux observed by Ginga in 1991 Nov.. An iron K$\alpha$ line is unambiguously detected, with an equivalent width of 170$\pm$90 eV (90\% confidence), and resolved . It has a centroid energy of 6.33$\pm$0.08 keV in the rest frame of the source, which is indicative of fluorescent emission from ``cold'' iron. The line width (FWHM of a Gaussian fit) is between 4,000 and 26,000 km~s$^{-1}$ with 90\% confidence. Alternatively, the line shape is consistent with that of the broad H$\alpha$ line whose double peaks are separated by 8,000 km~s$^{-1}$. However, the signal-to-noise ratio of the X-ray data is not sufficient for a detailed study of its line profile. If the line width is attributed to Keplerian motion, then the emitting gas is located a few hundred gravitational radii or more from the central massive object. If the Fe~K$\alpha$ line originates in an accretion disk with inclination angle $26^{\circ}$ (estimated independently from model fits to the double-peaked H$\alpha$ line, and from superluminal motions in the compact radio jet), then its measured equivalent width and centroid energy are in agreement with models for the reprocessing of X-rays from cool, dense material in the disk at a few hundred gravitational radii. An alternative origin of the Fe~K$\alpha$ line in the hot, innermost region of a disk is disfavored on the basis of the small velocity width, and centroid energy which is consistent with cold iron. It would also be difficult to attribute the X-ray line to fluorescence in ``standard'' broad-line region clouds because they would need to have $N_{\rm H} > 10^{23}$ cm$^{-2}$ and a large covering fraction, which is not supported by the unabsorbed nature of the X-ray continuum.
