||We use optical and near-infrared spectroscopy to observe rest-UV emission lines and estimate the black hole mass of WISEA J224607.56-052634.9 (W2246-0526) at z = 4.601, the most luminous hot, dust-obscured galaxy yet discovered by WISE. From the broad component of the Mg II 2799 A emission line, we measure a black hole mass of log(M-BH/M-circle dot)= 9.6 +/- 0.4. The broad C IV 1549 A line is asymmetric and significantly blueshifted. The derived M-BH from the blueshift-corrected broad C IV line width agrees with the Mg II result. From direct measurement using a well-sampled SED, the bolometric luminosity is 3.6 x 10(14) L-circle dot. The corresponding Eddington ratio for W2246-0526 is lambda(Edd) = L-AGN/L-Edd = 2.8. This high Eddington ratio may reach the level where the luminosity is saturating due to photon trapping in the accretion flow and may be insensitive to the mass accretion rate. In this case, the MBH growth rate in W2246-0526. would exceed the apparent accretion rate derived from the observed luminosity.