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We present a microscopic calculation of the 6He beta-decay into the ground state of 6Li. To this end, we use chiral perturbation theory at next-to-next-to-next-to-leading order to describe the nuclear weak-currents. The nuclear wave functions are derived from the J-matrix inverse scattering nucleon-nucleon potential (JISP), and the Schroedinger equation is solved using the hyperspherical-harmonics expansion. Our calculation brings the theoretical decay-rate within 3% of the measured one. This success is attributed to the use of chiral-perturbation-theory based mesonic currents, whose contribution is qualitatively different compared to standard nuclear physics approach, where the use of meson exchange currents worsens the comparison to experiment. The inherent inconsistency in the use of the JISP potential together with chiral-perturbation-theory based is argued not to affect this conclusion, though a more detailed investigation is called for. We conclude that any suppression of the axial constant in nuclear matter is included in this description of the weak interaction in the nucleus., Comment: Accepted for publication in Physical Review C