The masses of the neutron-rich radon isotopes {223-229}Rn have been determined for the first time, using the ISOLTRAP setup at CERN ISOLDE. In addition, this experiment marks the first discovery of a new nuclide, 229Rn, by Penning-trap mass measurement. The new, high-accuracy data allow a fine examination of the mass surface, via the valence-nucleon interaction deltaV{pn}. The results reveal intriguing behavior, possibly reflecting either a N=134 subshell closure or an octupolar deformation in this region.