High-resolution FUSE and STIS observations of the bright QSO HE 0226-4110 (z em= 0.495) reveal the presence of a multiphase absorption-line system at z abs (O)= 0.20701 containing absorption from HI (Lyα to Lyθ), C III, O III, O IV, O VI, N III, Ne VIII, Si III, S VI, and possibly S V. Single-component fits to the Ne VIII and O VI absorption doublets yield log N (Ne)= 13.89±0.11, b= 23±15 km s-1, and v=-7±6 km s-1 and log N (O)= 14.37±0.03, b= 31±2 km s-1, and v= 0±2 km s-1. The Ne VIII and O VI doublets are detected at 3.9 and 16 σ significance levels, respectively. This represents the first detection of intergalactic Ne VIII, a diagnostic of gas with temperature in the range from~ 5× 10 5 to~ 1× 10 6 K. Through the entire absorber, N (Ne)/N (O)= 0.33±0.10. The O VI and Ne VIII are not likely to have been created in a low-density medium photoionized solely by the extragalactic background at z= 0.2, since the required path length~ 11 Mpc (assuming [Z/H]=-0.5) implies that the Hubble flow absorption-line broadening would be~ 10 times greater than the observed line widths. A collisional ionization origin is therefore more likely. Assuming [Ne/H] and [O/H]=-0.5, the value N (Ne)/N (O)= 0.33±0.10 is consistent with gas in collisional ionization equilibrium near T= 5.4× 10 5 K with log N (H)= 19.9 and N (H)/N (H)= 1.7× 10 6. Various nonequilibrium ionization processes are also considered, because gas with T~(1-6)× 10 5 K cools efficiently. The observations of O VI and Ne VIII in the z= 0.20701 system support the basic idea that a substantial fraction of the baryonic matter at low redshift exists in hot, very highly ionized gaseous structures. Absorption by the moderately ionized gas (including O IV and S VI) is well modeled by gas in photoionization equilibrium with [Z/H]=-0.5±0.2, log U~-1.85, T~ 2.1× 10 4 K, n H~ 2.6× 10-5 cm-3, P/k~ 0.5 cm-3 K, and a path length of~ 60 kpc. These values suggest that the moderately ionized absorber may be associated with the modestly enriched photoionized gas in a galaxy group or the outermost regions of a galaxy halo.