Q0302 - 003 ( z = 3.2860 \pm 0.0005 ) was the first quasar discovered that showed a He ii Gunn-Peterson trough , a sign of incomplete helium reionization at z \gtrsim 2.9 . We present its HST /Cosmic Origins Spectrograph far-UV medium-resolution spectrum , which resolves many spectral features for the first time , allowing study of the quasar itself , the intergalactic medium , and quasar proximity effects . Q0302 - 003 has a harder intrinsic extreme-UV spectral index than previously claimed , as determined from both a direct fit to the spectrum ( yielding \alpha _ { \nu } \approx - 0.8 ) and the helium-to-hydrogen ion ratio in the quasar ’ s line-of-sight proximity zone . Intergalactic absorption along this sightline shows that the helium Gunn-Peterson trough is largely black in the range 2.87 < z < 3.20 , apart from ionization due to local sources , indicating that helium reionization has not completed at these redshifts . However , we tentatively report a detection of nonzero flux in the high-redshift trough when looking at low-density regions , but zero flux in higher-density regions . This constrains the He ii fraction to be about 1 % in the low-density IGM and possibly a factor of a few higher in the IGM as a whole , suggesting helium reionization has progressed substantially by z \sim 3.1 . The Gunn-Peterson trough recovers to a He ii Ly \alpha forest at z < 2.87 . We confirm a transmission feature due to the ionization zone around a z = 3.05 quasar just off the sightline , and resolve the feature for the first time . We discover a similar such feature possibly caused by a luminous z = 3.23 quasar further from the sightline , which suggests that this quasar has been luminous for > 34 Myr .