We have obtained the C-13 alpha chemical shift tensors for each amino acid in the protein GB1. We then developed a CST force field and incorporated this into the Xplor-NIH structure determination program. GB1 structures obtained by using CST restraints had improved precision over those obtained in the absence of CST restraints and were also more accurate. When combined with isotropic chemical shifts, distance, and vector angle restraints, the root-mean squared error with respect to existing X-ray structures was better than similar to 1.0 angstrom. These results are of broad general interest since they show that chemical shift tensors can be used in protein structure refinement, improving both structural accuracy and precision, opening up the way to accurate de novo structure determination.