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We report the first high resolution spectroscopic detection of H$2$NCO$+$, the protonated cation of isocyanic acid, in a discharge through HNCO heavily diluted in hydrogen in the throat of a supersonic nozzle. Spectroscopic constants derived from the two lowest rotational transitions agree very well with theoretical structure calculations of the ground state isomer, in which protonation occurs at the nitrogen atom, yielding an isomer of C symmetry. In the same molecular beam, the fundamental rotational transition of NCO$-$ was observed with well-resolved nitrogen quadrupole hyperfine structure. Detection of NCO$-$ in our beam was subsequently confirmed by observation of several millimeter-wave transitions in a low pressure discharge through cyanogen and water. The spectroscopic constants of NCO$-$ obtained earlier by infrared laser spectroscopy nderline{\textbf{86}}, 6631, (1987).} are in good agreement with the highly accurate constants derived here. Owing to the high abundance of HNCO in many galactic molecular sources, both ions are excellent candidates for astronomical detection in the radio band. %The rotational spectrum of H$2$NCO$+$ has been recently detected in a supersonic molecular beam. through the discharge of isocyanic acid heavily diluted in a hydrogen expansion. Under the same experimental conditions, the fundamental rotational transition of NCO$-$ has also been observed, showing the expected hyperfine structure from the presence of the nitrogen nucleus. The laboratory search has been guided by high level quantum chemical calculations and the rotational constant derived by infrared laser spectroscopy nderline{\textbf{86}}(12), 6631 June 1987.} for the anion. Due to the high abundance of HNCO in several interstellar medium regions, these two molecular ions represent serious candidates for detection through radio-astronomical techniques. %By means of high resolution microwave techniques, the spectra of NCO$-$ and H$2$NCO$+$ has been recently detected. The laboratory search of the cation has been guided by theoretical structure calculations performed at the CCSD(T)/cc-pwCVQZ level of theory corrected for zero-point vibrational effects at the CCSD(T)/cc-pVQZ level. The anion search has been based on the rotational constant derived by infrared laser spectroscopy nderline{\textbf{86}}(12), 6631 June 1987.} and the nitrogen quadrupole coupling constant calculated at the CCSD(T)/aug-cc-pwCVQZ level of theory. Both species have produced using isocyanic acid heavily diluted in a hydrogen expansion. The spectrum of both ions shows expected hyperfine structure from the presence of the nitrogen nucleus, providing a crucial confirmation of the discovery. Due to the large and ubiquitous presence of isocyanic acid in several interstellar medium regions, these two molecular ions represent serious candidates for detection through radio-astronomical techniques.