Dielectronic recombination (DR) of xenonlike W20+ forming W19+ has been studied experimentally at a heavy-ion storage-ring. A merged-beams method has been employed for obtaining absolute rate coefficients for electron-ion recombination in the collision energy range 0-140 eV. The measured rate coefficient is dominated by strong DR resonances even at the lowest experimental energies. At plasma temperatures where the fractional abundance of W20+ is expected to peak in a fusion plasma, the experimentally derived plasma recombination rate coefficient is over a factor of 4 larger than the theoretically-calculated rate coefficient which is currently used in fusion plasma modeling. The largest part of this discrepancy stems most probably from the neglect in the theoretical calculations of DR associated with fine-structure excitations of the W20+([Kr] 4d10 4f8) ion core.