The pure rotational spectrum of the X (1)Sigma(+) ground electronic state of yttrium monobromide has been measured. This is the first high-resolution spectrum recorded for this molecule. Transitions in the ground and first excited vibrational states have been measured for both the (YBr)-Br-79 and (YBr)-Br-81 isotopomers. Equilibrium rotational parameters have been determined and an equilibrium bond distance has been calculated. Vibrational parameters have been estimated. Hyperfine structure due to the bromine nuclei has been observed and nuclear quadrupole and nuclear spin-rotation constants have been determined. These parameters have been used to investigate the ionic character of the Y-Br bond and comparisons have been made to several alkali and alkaline earth metal bromide species.