  There is a significant discrepancy between the current theoretical prediction
of the cosmological lithium abundance, mostly produced as Be7 during the Big
Bang, and its observationally inferred value. We investigate whether the
resonant enhancement of Be7 burning reactions may alleviate this discrepancy.
We identify one narrow nuclear level in B9, E_{5/2^+} \simeq 16.7 MeV that is
not sufficiently studied experimentally, and being just \sim 200 keV above the
Be7+d threshold, may lead to the resonant enhancement of Be7(d,\gamma)B9 and
Be7(d,p)\alpha\alpha reactions. We determine the relationship between the
domain of resonant energies E_r and the deuterium separation width \Gamma_d
that results in the significant depletion of the cosmological lithium abundance
and find that (E_r, ~\Gamma_{d}) \simeq (170-220,~10-40) keV can eliminate
current discrepancy. Such a large width at this resonant energy can be only
achieved if the interaction radius for the deterium entrance channel is very
large, a_{27} \ge 9 fm. Our results also imply that before dedicated nuclear
experimental and theoretical work is done to clarify the role played by this
resonance, the current conservative BBN prediction of lithium abundance should
carry significantly larger error bars, [Li7/H]_{\rm BBN} = (2.5-6)\times
10^{-10}.
