The neutral hydrogen (H I) and ionized helium (He II) absorption in the spectra of quasars are unique probes of structure in the early universe. We present Far-Ultraviolet Spectroscopic Explorer observations of the line of sight to the quasar HE2347-4342 in the 1000 to 1187 angstrom band at a resolving power of 15,000. We resolve the He II Lyman alpha (Lyalpha) absorption as a discrete forest of absorption lines in the redshift range 2.3 to 2.7. About 50 percent of these features have H I counterparts with column densities N(H I) > 10(12.3) per square centimeter that account for most of the observed opacity in He II Lyalpha. The He II to H I column density ratio ranges from 1 to >1000, with an average of approximately 80. Ratios of <100 are consistent with photoionization of the absorbing gas by a hard ionizing spectrum resulting from the integrated light of quasars, but ratios of >100 in many locations indicate additional contributions from starburst galaxies or heavily filtered quasar radiation. The presence of He II Lyalpha absorbers with no H I counterparts indicates that structure is present even in low-density regions, consistent with theoretical predictions of structure formation through gravitational instability.