On two occasions, we obtained nearly simultaneous ~=4 ks snapshot observations of the Galactic black hole and microquasar XTE J1550-564 with Chandra and RXTE near the peak of its 2000 May outburst. The low-energy sensitivity of Chandra and the resolution of the High Energy Transmission Grating Spectrometer (HETGS), coupled with the broad energy range and large collecting area of RXTE, have allowed us to place constraints on the outburst accretion flow geometry of this source in the `intermediate' X-ray state. The 0.65-25.0 keV continuum spectra are well described by a relatively hot (kT~= 0.8 keV) accretion disc and hard (Γ~= 2.3) coronal power-law components. Broad, relatively strong Fe Kα emission line (WKα~= 170 eV) and smeared absorption edge components consistent with FeXXV are strongly required in joint spectral fits. The resolution of the Chandra/HETGS reveals that the broad Fe Kα emission lines seen clearly in the individual RXTE spectra are not the result of an intrinsically narrow line.