We show that Shubnikov-de Haas oscillations in the interlayer resistivity of the organic superconductor beta(")-(BEDT-TTF)2SF5CH2CF2SO3 become very pronounced in magnetic fields approximately 60 T. The conductivity minima exhibit thermally activated behavior that can be explained simply by the presence of a Landau gap, with the quasi-one-dimensional Fermi surface sheets contributing negligibly to the conductivity. This observation, together with complete suppression of chemical potential oscillations, is consistent with an incommensurate nesting instability of the quasi-one-dimensional sheets.