  It has been pointed out by Shlyakhter that data from the natural fission
reactors which operated about two billion years ago at Oklo (Gabon) had the
potential of providing an extremely tight bound on the variability of the
fine-structure constant alpha. We revisit the derivation of such a bound by:
(i) reanalyzing a large selection of published rare-earth data from Oklo, (ii)
critically taking into account the very large uncertainty of the temperature at
which the reactors operated, and (iii) connecting in a new way (using isotope
shift measurements) the Oklo-derived constraint on a possible shift of thermal
neutron-capture resonances with a bound on the time variation of alpha. Our
final (95% C.L.) results are:
  -0.9 \times 10^{-7} <(alpha^{Oklo} - alpha^{now})/alpha <1.2\times 10^{-7}
  and -6.7 \times 10^{-17} {yr}^{-1} < {\dot alpha}^{averaged}/alpha
<5.0\times10^{-17} {yr}^{-1}$.
