An attempt was made to measure the excitation function of the cross section for the Li-8(n,gamma)Li-9 reaction by performing the inverse reaction Li-9(gamma,n)Li-8, with the equivalent photons in the electric field of nuclei in a Pb target providing the gamma rays for the reaction. The energy spectrum of lithium nuclei in coincidence with neutrons had no discernible peak where any beam-velocity Li-8`s would be located. Statistically, a Gaussian-shaped Li-8 peak could have been present with 30+/-29 counts, which we interpreted as consistent with zero, with a two-standard-deviation upper limit of 87 counts. Using the fact that neutron capture on Li-8 must be dominantly s-wave capture, and applying detailed balance, we obtained, with E in eV, sigma(n,gamma)<930E(-1/2) mu b. The corresponding limit on the astrophysical reaction rate is <790 cm(3) mol(-1) s(-1). Theoretical predictions of the reaction rate have exceeded our upper limit by factors of 3-50.