The intersections are (12/13*(3*sqrt(3) - 1),6/13*(3 + 4*sqrt(3)) and (-12/13*(1 + 3sqrt(3)), -6/13*(4*sqrt(3) - 3), so the length of the chord is sqrt((12/13*(3*sqrt(3) - 1 + 12/13*(1 + 3*sqrt(3))^2 + (6/13*(3 + 4*sqrt(3)) + 6/13*(4*sqrt(3) - 3))^2) = 24*sqrt(39)/13.
