One-dimensional localized plasmons (channel polaritons) guided by a triangular groove on a metal substrate are investigated numerically by means of a finite-difference time-domain algorithm. Dispersion, existence conditions, and dissipation of these waves are analyzed. In particular, it is demonstrated that the localization of the predicted plasmons in acute grooves may be substantially stronger than what is allowed by the diffraction limit. As a result, the predicted waves may be significant for the development of new subwavelength waveguides and interconnectors for nano-optics and photonics.