While the Lyman α (Ly α) emission line serves as an important tool in the study of galaxies at z ≲ 6, finding Ly α emitters (LAE) at significantly higher redshifts has been more challenging, probably because of the increasing neutrality of the intergalactic medium above z ∼ 6. Galaxies with extremely high rest-frame Ly α equivalent widths, EW(Ly α) ≳ 150 Å, at z > 6, are good candidates for Ly α follow-up observations, and can stand out in multiband imaging surveys because of their unusual colours. We have conducted a photometric search for such objects in the Cluster Lensing And Supernova survey with Hubble (CLASH), and report here the identification of three likely gravitationally lensed images of a single LAE candidate at z ∼ 6.3, behind the galaxy cluster Abell 2261 (z = 0.225). In the process, we also measured with Keck/Multi-Object Spectrometer For Infra-Red Exploration the first spectroscopic redshift of a multiply imaged galaxy behind Abell 2261, at z = 3.337. This allows us to calibrate the lensing model, which, in turn, is used to study the properties of the candidate LAE. Population III galaxy spectral energy distribution model fits to the CLASH broad-band photometry of the possible LAE provide a slightly better fit than Population I/II models. The best-fitting model suggests intrinsic EW(Ly α) ≈160 Å after absorption in the interstellar and intergalactic medium. Future spectroscopic observations will examine this prediction as well as shed more light on the morphology of this object, which indicates that it may be a merger of two smaller galaxies.