  We analyse high-resolution near-UV and optical spectra of the afterglow of
GRB 080310, obtained with the Very Large Telescope Ultraviolet and Visual
Echelle Spectrograph (VLT/UVES), to investigate the circumburst environment and
the interstellar medium of the gamma-ray burst (GRB) host galaxy. The VLT
rapid-response mode (RRM) enabled the observations to start only 13 minutes
after the Swift trigger and a series of four exposures to be collected before
dawn. A low neutral-hydrogen column-density (log N (HI) = 18.7) is measured at
the host-galaxy redshift of z = 2.42743. At this redshift, we also detect a
large number of resonance ground-state absorption lines (e.g., CII, MgII, AlII,
SiII, CrII, CIV, SiIV), as well as time-varying absorption from the
fine-structure levels of FeII. Time-varying absorption from a highly excited
FeIII energy level (7S3), giving rise to the so-called UV34 line triplet, is
also detected, for the first time in a GRB afterglow. The CrII ground-state and
all observed FeII energy levels are found to depopulate with time, whilst the
FeIII 7S3 level is increasingly populated. This absorption-line variability is
clear evidence of ionization by the GRB, which is for the first time
conclusively observed in a GRB afterglow spectrum. We derive ionic column
densities at each epoch of observations by fitting absorption lines with a
four-component Voigt-profile model. We perform CLOUDY photo-ionization
modelling of the expected pre-burst ionic column densities, to estimate that,
before the onset of the burst, [C/H] = -1.3 \pm 0.2, [O/H] < -0.8, [Si/H] =
-1.2 \pm 0.2, [Cr/H] = +0.7 \pm 0.2, and [Fe/H] = +0.2 \pm 0.2 for the
integrated line profile, indicating strong overabundances of iron and chromium.
For one of the components, we observe even more extreme ratios of [Si/Fe] \leq
-1.47 and [C/Fe] \leq -1.74. [abridged]
