The galaxy cluster IDCS J1426.5+3508 at z = 1.75 is the most massive galaxy cluster yet discovered at z > 1.4 and the first cluster at this epoch for which the Sunyaev-ZelDovich effect has been observed. In this paper we report on the discovery with HST imaging of a giant arc associated with this cluster. The curvature of the arc suggests that the lensing mass is nearly coincident with the brightest cluster galaxy, and the color is consistent with the arc being a star-forming galaxy. We compare the constraint on M200 based upon strong lensing with Sunyaev-ZelDovich results, finding that the two are consistent if the redshift of the arc is z > 3. Finally, we explore the cosmological implications of this system, considering the likelihood of the existence of a strongly lensing galaxy cluster at this epoch in an LCDM universe. While the existence of the cluster itself can potentially be accomodated if one considers the entire volume covered at this redshift by all current high-redshift cluster surveys, the existence of this strongly lensed galaxy greatly exacerbates the long-standing giant arc problem. For standard LCDM structure formation and observed background field galaxy counts this lens system should not exist. Specifically, there should be no giant arcs in the entire sky as bright in F814W as the observed arc for clusters at z geq 1.75, and only sim 0.3 as bright in F160W as the observed arc. If we relax the redshift constraint to consider all clusters at z geq 1.5, the expected number of giant arcs rises to sim15 in F160W, but the number of giant arcs of this brightness in F814W remains zero. These arc statistic results are independent of the mass of IDCS J1426.5+3508. We consider possible explanations for this discrepancy.
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