  We report ultraviolet spectra of the high-redshift (z_em = 2.9) quasar, HE
2347-4342, taken by the Cosmic Origins Spectrograph (COS) on the Hubble Space
Telescope (HST). Spectra in the G130M (medium-resolution, 1135-1440 A) and
G140L (low-resolution, 1030-2000 A) gratings exhibit patchy Gunn-Peterson
absorption in the 303.78 A (Ly-alpha) line of He II between z = 2.39-2.87
(G140L) and z = 2.74-2.90 (G130M). With COS, we obtain better spectral
resolution, higher-S/N, and better determined backgrounds than previous
studies, with sensitivity to abundance fractions x_HeII = 0.01 in filaments of
the cosmic web. The He II optical depths from COS are higher than those with
the Far Ultraviolet Spectroscopic Explorer (FUSE) and range from tau_HeII <
0.02 to tau_HeII > 5, with a slow recovery in mean optical depth, tau < 2 at z
< 2.7. The He II/H I optical-depth ratio varies (eta = 10-100 for 2.4 < z <
2.73 and eta = 5-500 for 2.75 < z < 2.89) on scales Delta z < 0.01 (10.8 Mpc in
comoving radial distance at z = 2.8), with numerous flux-transmission windows
between 1135-1186 A. The He II absorption extends to 1186.26 A (z = 2.905),
including associated absorbers with z_abs ~ z_QSO and minimal "proximity
effect" of flux transmission at the He II edge. We propose a QSO systemic
redshift z_QSO = 2.904 +/- 0.002, some Delta z = 0.019 higher than that derived
from O I (1302 A) emission. Three long troughs (4-10 A or 25-60 Mpc comoving
distance) of strong He II absorption between z = 2.75-2.90 are uncharacteristic
of the intergalactic medium if He II reionized at z_r ~ 3. Contrary to recent
indirect estimates (z_r = 3.2 +/- 0.2) from H I optical depths, the epoch of
HeII reionization may extend to z ~ 2.7.
