  A new molecular hydrogen cloud is found in the sub-damped Ly-alpha absorber
[log N(HI)=19.88+/-0.05] at the redshift z=1.15 toward the bright quasar
HE0515-4414 (zem = 1.71). More than 30 absorption features in the Lyman band
system of H2 are identified in the UV spectrum of this quasar obtained with the
Space Telescope Imaging Spectrograph (STIS) aboard the Hubble Space Telescope.
The H2-bearing cloud shows a total H2 column density N(H2)=(8.7^{+8.7}_-{4.0})
10^16 cm^-2, and a fractional molecular abundance f(H2)=(2.3^{+2.3}_{-1.1})
10^-3 derived from the H2 lines arising from the J=0-5 rotational levels of the
ground electronic vibrational state. The estimated rate of photodissociation at
the cloud edge I_0<=1.8 10^{-8} s^-1 is much higher than the mean Galactic disk
value, I_MW~=5.5 10^{-11} s^-1. This may indicate an enhanced star-formation
activity in the z=1.15 system as compared with molecular clouds at z~=3 where
I~=I_MW. We also find a tentative evidence that the formation rate coefficient
of H2 upon grain surfaces at z=1.15 is a factor of 10 larger than a canonical
Milky Way value, R_MW~=3 10^-17 cm^3 s^-1. The relative dust-to-gas ratio
estimated from the [Cr/Zn] ratio is equal to k=0.89+/-0.19 (in units of the
mean Galactic disk value), which is in good agreement with a high molecular
fraction in this system. The estimated line-of-sight size of L~=0.25 pc may
imply that the H2 is confined within small and dense filaments embedded in a
more rarefied gas giving rise to the z=1.15 sub-damped Ly-alpha absorber.
