We present the first acoustic vibration measurements of single gold nanorods with well-characterized dimensions and crystal structure. The nanorods have an average size of 90 nm x 30 nm and display two vibration modes, the breathing mode and the extensional mode. Correlation between the dimensions obtained from electron microscope images and the vibrational frequencies of the same particle allows us to determine the elastic moduli for each individual nanorod. Contrary to previous reports on ensembles of gold nanorods, we find that the single particle elastic moduli agree well with bulk values.