The plasmonic properties of single silver triangular nanoprisms are investigated using dark-field optical microscopy and spectroscopy. Two distinct localized surface plasmon resonances (LSPR) are observed. These are assigned as in-plane dipolar and quadrupolar plasmon excitations using electrodynamic modeling based on the discrete dipole approximation (DDA). The dipole resonance is found to be very intense, and its peak wavelength is extremely sensitive to the height, edge length, and tip sharpness of the triangular nanoprism. In contrast, the intensity of the quadrupole resonance is much weaker relative to the dipole resonance in the single particle spectra than in the ensemble averaged spectrum. Several parameters relevant to the chemical sensing properties of these nanoprisms have been measured. The dependence of the dipole plasmon resonance on the refractive index of the external medium is found to be as high as 205 nm RIU(-1) and the plasmon line width as narrow as approximately 0.17 eV. These data lead to a sensing figure of merit (FOM), the slope of refractive index sensitivity in eV RIU(-1)/line width (eV), as high as 3.3. In addition, the LSPR shift response to alkanethiol chain length was found to be linear with a slope of 4.4 nm per CH2 unit. This is the highest short-range refractive index sensitivity yet measured for a nanoparticle.