The neutron unbound ground state of (25)O (Z=8, N=17) was observed for the first time in a proton knockout reaction from a (26)F beam. A single resonance was found in the invariant mass spectrum corresponding to a neutron decay energy of 770_+20(-10) keV with a total width of 172(30) keV. The N=16 shell gap was established to be 4.86(13) MeV by the energy difference between the nu1s(1/2) and nu0d(3/2) orbitals. The neutron separation energies for (25)O agree with the calculations of the universal sd shell model interaction. This interaction incorrectly predicts an (26)O ground state that is bound to two-neutron decay by 1 MeV, leading to a discrepancy between the theoretical calculations and experiment as to the particle stability of (26)O. The observed decay width was found to be on the order of a factor of 2 larger than the calculated single-particle width using a Woods-Saxon potential.