Since galaxy clusters sit at the high end of the mass function, the number of galaxy clusters both massive and concentrated enough to yield particularly large Einstein radii poses useful constraints on cosmological and structure formation models. To date, less than a handful of clusters are known to have Einstein radii exceeding ~40" (for a source at z_s_~2, nominally). Here, we report an addition to that list of the Sunyaev-Zel'dovich (SZ) selected cluster, PLCKG287.0+32.9 (z=0.38), the second-highest SZ-mass (M500) cluster from the Planck catalog. We present the first strong-lensing analysis of the cluster, identifying 20 sets of multiply imaged galaxies and candidates in new Hubble Space Telescope (HST) data, including a long, l~22" giant arc, as well as a quadruply imaged, apparently bright (magnified to J_F110W_=25.3 AB), likely high-redshift dropout galaxy at z_phot_=6.90 [6.13-8.43] (95% C.I.). Our analysis reveals a very large critical area (1.55arcmin^2^, z_s_~2), corresponding to an effective Einstein radius of {theta}_E_~42". The model suggests the critical area will expand to 2.58arcmin^2^ ({theta}_E_~54") for sources at z_s_~10. Our work adds to recent efforts to model very massive clusters toward the launch of the James Webb Space Telescope, in order to identify the most useful cosmic lenses for studying the early universe. Spectroscopic redshifts for the multiply imaged galaxies and additional HST data will be necessary for refining the lens model and verifying the nature of the z~7 dropout.