The internal symmetries of the Escherichia coli molecular chaperone cpn60 oligomer, also called GroEL, have been examined by X-ray crystallography and self-rotation functions calculated at a resolution of 8.9 A. The oligomer ([cpn60]14) has one 7-fold symmetry axis and seven 2-fold axes that are all perpendicular to the 7-fold. The symmetry can be explained if oligomeric cpn60 is arranged as two heptamers stacked on top of each other, where the heptameric arrangement generates the 7-fold symmetry axis and the head-to-head assembly of two heptamers results in the seven 2-fold axes. This is an agreement with interpretations of electron microscopy data. However, the experimental determination of the symmetries reported here are made with an independent technique and at higher resolution. In addition self-rotation function calculations show that the symmetries observed are valid also for the internal parts of GroEL and not only for surface views. The orientations of the symmetry axes of the two independent cpn60 oligomers in the triclinic unit cell have been determined relative to the crystallographic axes. The planes formed by the 2-fold axes in the two oligomers deviate by about 2 degrees from the plane formed by the crystallographic a and c axes, while the 7-fold axes form angles of about 16 degrees with the b-axis. The two oligomers in the unit cell are arranged with their 7-fold axis parallel, but the second oligomer is rotated 26 degrees around the 7-fold axis relative to the first oligomer. Knowledge of the symmetry and orientation of the oligomers in the unit cell will be of great help in further crystallographic work.