Ab initio density functional theory (DFT) is used to analyze the vibrational unpolarized absorption and circular dichroism spectra of the chiral monoterpene, alpha-pinene. Large (TZ2P) basis set calculations using the hybrid functionals B3PW91 and B3LYP are in excellent overall agreement with experiment and permit the assignment of a large fraction of the fundamental frequencies, The quantitative accuracy of DFT in predicting the frequencies, dipole strengths, and rotational strengths of the fundamentals of alpha-pinene is documented for the B3PW91 and B3LYP functionals at both TZ2P and 6-31G* basis set levels. Hartree-Fock/self-consistent field (HF/SCF) calculations have also been carried out in parallel. The accuracy of the HF/SCF methodology is markedly inferior to that of DFT. In particular, HF/SCF predictions of the vibrational circular dichroism (VCD) spectrum of alpha-pinene are in very poor agreement with experiment.