The fraction of ionizing photons ( f _ { \mathrm { esc } } ) that escape from z \gtrsim 6 galaxies is an important parameter when assessing the role of these objects in the reionization of the Universe , but the opacity of the intergalactic medium precludes a direct measurement of f _ { \mathrm { esc } } for individual galaxies at these epochs . We argue , that since f _ { \mathrm { esc } } regulates the impact of nebular emission on the spectra of galaxies , it should nonetheless be possible to indirectly probe f _ { \mathrm { esc } } well into the reionization epoch . As a first step , we demonstrate that by combining measurements of the rest-frame UV slope \beta with the equivalent width of the H \beta emission line , galaxies with very high Lyman continuum escape fractions ( f _ { \mathrm { esc } } \geq 0.5 ) should be identifiable up to z \approx 9 through spectroscopy with the upcoming James Webb Space Telescope ( JWST ) . By targeting strongly lensed galaxies behind low-redshift galaxy clusters , JWST spectra of sufficiently good quality can be obtained for M _ { 1500 } \lesssim - 16.0 galaxies at z \approx 7 and for M _ { 1500 } \lesssim - 17.5 galaxies at z \approx 9 . Dust-obscured star formation may complicate the analysis , but supporting observations with ALMA or the planned SPICA mission may provide useful constraints on the dust properties of these galaxies .