  We calculate the form factor f_+(q^2) for B-meson semileptonic decay in
unquenched lattice QCD with 2+1 flavors of light sea quarks. We use
Asqtad-improved staggered light quarks and a Fermilab bottom quark on gauge
configurations generated by the MILC Collaboration. We simulate with several
light quark masses and at two lattice spacings, and extrapolate to the physical
quark mass and continuum limit using heavy-light meson staggered chiral
perturbation theory. We then fit the lattice result for f_+(q^2) simultaneously
with that measured by the BABAR experiment using a parameterization of the form
factor shape in q^2 which relies only on analyticity and unitarity in order to
determine the CKM matrix element |V(ub)|. This approach reduces the total
uncertainty in |V(ub)| by combining the lattice and experimental information in
an optimal, model-independent manner. We find a value of |V(ub)| x 10^3 = 3.38
+/- 0.36.
