The absolute cross section for the reaction, He^3(α,γ) Be^7, hasbeen measured over the range of energies 181 ≤ E_(cm) ≤ 2493 keV, usinga gas target behind a thin nickel entrance foil. Calibrated NaI(Tl)crystals were used to detect the prompt capture radiation. Over theentire energy region the measured total cross section and branchingratio confirm theoretical predictions based on calculations neglectingthe contributions to the matrix elements from the region inside thenuclear radius. These cross-section measurements have been usedto obtain a new value for the low-energy cross-section factor, S_o, forthis reaction (S_o = 0.47 ± .07 keY barns), and this value has been usedto reevaluate the importance of the He^3(α,γ) Be^7 reaction in the termination of the proton-proton chain in nuclear astrophysics.