A Large Isotopic Composition Experiment (ALICE) is a balloon-borne spectrometer which can determine the elemental and isotopic composition of galactic cosmic rays with energies near 1 GeV/nucleon. ALICE was flown from Prince Albert, Canada in August 1987, and remained at float altitude (120000 feet) for 14.7 hours. In this paper, we describe the experimental methods and analysis which will be used for subsequent isotopic analysis. We obtained very precise charge resolution over the entire designed range: 0.10 and 0.16 charge units at neon and iron, respectively. Results on the galactic cosmic ray abundances and absolute fluxes of the elements from neon through nickel are reported.