  By combining the first unquenched lattice computation of the B-meson binding
energy and the two-loop contribution to the lattice HQET residual mass, we
determine the (\bar{{MS}}) (b)-quark mass, (\bar{m}_{b}(\bar{m}_{b})). The
inclusion of the two-loop corrections is essential to extract
(\bar{m}_{b}(\bar{m}_{b})) with a precision of ({\cal
O}(\Lambda^{2}_{QCD}/m_{b})), which is the uncertainty due to the renormalon
singularities in the perturbative series of the residual mass. Our best
estimate is (\bar{m}_{b}(\bar{m}_{b}) = (4.26 \pm 0.09) {\rm GeV}), where we
have combined the different errors in quadrature. A detailed discussion of the
systematic errors contributing to the final number is presented. Our results
have been obtained on a sample of (60) lattices of size (24^{3}\times 40) at
(\beta =5.6), using the Wilson action for light quarks and the lattice HQET for
the (b) quark, at two values of the sea quark masses. The quark propagators
have been computed using the unquenched links generated by the T(\chi)L
Collaboration.
