Contracted Gaussian basis sets of triple zeta valence (TZV) quality are presented for Li to Kr. The TZV bases are characterized by typically including a single contraction to describe inner shells and three basis functions for valence shells. All parameters-orbital exponents and contraction coefficients-have been determined by minimization of atomic self-consistent field ground state energies. Advantages and necessary modifications of TZV basis sets are discussed for simple test calculations of molecular energies and nuclear magnetic resonance (NMR) chemical shieldings in treatments with and without inclusion of electron correlation.