X-ray absorption fine structure (XAFS) spectroscopy was used to probe the effects of concentration on the first-shell structure of Ca2+ in aqueous solution. Measurements were carried out under ambient conditions using a bending magnet beamline (sector 20) at the Advanced Photon Source, Argonne. The Ca K-edge EXAFS spectrum for 6 m CaCl2 yielded no evidence for the formation of significant numbers of Ca2+-Cl- contact ion pairs even at such high concentration, a result confirmed by comparison with the data for a dilute (0.2 m) reference solution of the perchlorate. A mean coordination number of 7.2 +/- 1.2 water molecules and an average Ca-O distance of 2.437 +/- 0.010 Angstrom were determined for 6 m CaCl2, and these parameters are also consistent with earlier EXAFS measurements on dilute Ca2+ solutions. Comparison of the pre-edge and near-edge (XANES) spectrum against those for various references, including the crystalline hydrates, provided further confirmation of the lack of change in the Ca2+ first-shell structure and symmetry. Our measurements help clarify the earlier results of modeling thermodynamic data that imply that some significant structural change occurs at high salt concentration. Taken together, our results suggest the formation of Ca2+-OH2-Cl- solvent-shared ion pairs, rather than Ca2+-Cl- contact ion pairs, is most likely responsible for the unusual thermodynamic behavior of this system. The EXAFS spectrum for an even more concentrated (9.2 m CaCl2) hexahydrate melt, however, did indicate the presence of some contact ion pairs. The new results agree closely with those of an earlier X-ray diffraction study, and serve to further aid interpretation of the aqueous solutions data. On a technical note, a previously unreported multielectron excitation edge at k = 10.2 Angstrom(-1) was detected in the EXAFS spectra and assigned to the KLII,III transition. Inclusion of this new transition, along with the other known (KMII,III and KMI) transitions, in the background correction procedure significantly improved the quality of EXAFS fits. Further improvements resulted from the inclusion of Ca-H single scattering paths to treat the protons on the tightly bound water molecules. A Ca-H distance of 2.97 Angstrom was obtained, which is in excellent agreement with the results of neutron scattering measurements (reported in part II). This appears to be the most convincing evidence to date for the detection of proton backscattering in EXAFS measurements of the local structure around ions in aqueous solution.