We report the detection of CO(2-1) emission coincident with the brightest cluster galaxy (BCG) of the high-redshift galaxy cluster SpARCS1049+56, with the Redshift Search Receiver (RSR) on the Large Millimetre Telescope (LMT). We confirm a spectroscopic redshift for the gas of z = 1.7091+/-0.0004, which is consistent with the systemic redshift of the cluster galaxies of z = 1.709. The line is well-fit by a single component Gaussian with a RSR resolution-corrected FWHM of 569+/-63 km/s. We see no evidence for multiple velocity components in the gas, as might be expected from the multiple image components seen in near-infrared imaging with the Hubble Space Telescope. We measure the integrated flux of the line to be 3.6+/-0.3 Jy km/s and, using alpha_CO = 0.8 Msun (K km s^-1 pc^2)^-1 we estimate a total molecular gas mass of 1.1+/-0.1x10^11 Msun and a M_H2/M_star ~ 0.4. This is the largest gas reservoir detected in a BCG above z > 1 to date. Given the infrared-estimated star formation rate of 860+/-130 Msun/yr, this corresponds to a gas depletion timescale of ~0.1Gyr. We discuss several possible mechanisms for depositing such a large gas reservoir to the cluster center -- e.g., a cooling flow, a major galaxy-galaxy merger or the stripping of gas from several galaxies -- but conclude that these LMT data are not sufficient to differentiate between them.