We present a new , high resolution HST/GHRS spectrum of quasar Q0302-003 , and use the He ^ { + } Lyman- \alpha absorption , together with a high resolution Keck spectrum of the HI Lyman- \alpha forest , to probe the distribution and ionization state of foreground gas just below the quasar redshift z \approx 3.3 . Within \approx 4000 km/sec of the quasar redshift the spectrum shows a substantial flux ( \tau \approx 1 ) with “ He ^ { + } Lyman- \alpha forest ” absorption features correlated in redshift with the HI Lyman- \alpha forest ; the absorption in this region is accounted for entirely by the discrete components of the forest , indeed the main “ Gunn-Peterson edge ” can be identified with a particular complex of HI absorbing clouds . We attribute the lack of continuous absorption from diffuse gas to the “ proximity effect ” in this region , a large bubble where helium is highly ionized by the quasar , and use its size to estimate the background flux at the He ^ { + } ionization threshold . The near-quasar data also lead to constraints on diffuse gas density near the quasar , tied to the observed quasar flux , and helium abundance , tied to the observed quasar spectrum . Far from the quasar redshift , the spectrum displays He ^ { + } absorption ( \tau \geq 1.3 ) even in several redshift intervals with no detectable HI absorption , implying a soft ionizing spectrum as well as absorption from gas between detected HI clouds . The smoothed spectrum displays residual flux everywhere with an average optical depth \tau _ { GP } \leq 2 , which indicates a low density of redshift-space-filling gas ; using constraints from the HI ionizing spectrum we estimate \Omega _ { g } \leq 0.01 ( h / 0.7 ) ^ { -1.5 } , and infer that the helium is already mostly doubly ionized by this epoch . Our estimates are consistent with ionization models based on observed quasar populations , previous limits from HI Gunn-Peterson studies , and simulations of the gas distribution in CDM models of galaxy formation .