We present the first results of a narrow-band photometric study of the massive galaxy cluster XMMU J2235.3-2557 at z= 1.39. We obtained deep H narrow-band imaging with the Near InfraRed Imager and Spectrometer on Gemini North, corresponding to Hα emission at the cluster's redshift. Our sample consists of 82 galaxies within a radius of ˜500 kpc, 10 of which are spectroscopically confirmed cluster members. 16 galaxies are identified as excess line-emitters. Among just the excess line-emitting galaxies, we find an average star formation rate (SFR) of 3.6 ± 1.3 M&sun; yr-1. For spectroscopically confirmed cluster members, we find a correlation between H broad-band magnitude and SFR such that brighter galaxies have lower SFRs. The probability that the SFR and magnitude of confirmed members are uncorrelated is 0.7 per cent. We also find a correlation between the SFR and distance from the cluster centre for both confirmed and excess line-emitting candidate members, with a probability of 5 per cent for there to be no correlation among confirmed members. All excess line-emitting candidate cluster members are located outside a radius of 200 kpc. We conclude that star formation is effectively shut off within the central 200 kpc radius (RQUENCH˜ 200 kpc) of this massive galaxy cluster at z= 1.39, when the Universe was only 4.5 Gyr old.