We present the discovery of four surprisingly bright (H160 ∼ 26-27 mag AB) galaxy candidates at z ∼ 9-10 in the complete HST CANDELS WFC3/IR GOODS-N imaging data, doubling the number of z ∼ 10 galaxy candidates that are known, just ∼500 Myr after the big bang. Two similarly bright sources are also detected in a reanalysis of the GOODS-S data set. Three of the four galaxies in GOODS-N are significantly detected at 4.5σ-6.2σ in the very deep Spitzer/IRAC 4.5 μm data, as is one of the GOODS-S candidates. Furthermore, the brightest of our candidates (at z = 10.2 ± 0.4) is robustly detected also at 3.6 μm (6.9σ), revealing a flat UV spectral energy distribution with a slope β = -2.0 ± 0.2, consistent with demonstrated trends with luminosity at high redshift. Thorough testing and use of grism data excludes known low-redshift contamination at high significance, including single emission-line sources, but as-yet unknown low redshift sources could provide an alternative solution given the surprising luminosity of these candidates. Finding such bright galaxies at z ∼ 9-10 suggests that the luminosity function for luminous galaxies might evolve in a complex way at z > 8. The cosmic star formation rate density still shows, however, an order-of-magnitude increase from z ∼ 10 to z ∼ 8 since the dominant contribution comes from low-luminosity sources. Based on the IRAC detections, we derive galaxy stellar masses at z ∼ 10, finding that these luminous objects are typically 109 M⊗. This allows for a first estimate of the cosmic stellar mass density at z ∼ 10 resulting in log10p∗ = 4.7+0.5-0.8 M⊗ Mpc-3 for galaxies brighter than Muv ∼ -18. The remarkable brightness, and hence luminosity, of these z ∼ 9-10 candidates will enable deep spectroscopy to determine their redshift and nature, and highlights the opportunity for the James Webb Space Telescope to map the buildup of galaxies at redshifts much earlier than z ∼ 10.