This paper presents the first direct measurement of the B meson differential cross section d sigma/d(pT) in <(pp)over bar> collisions at root s = 1.8 TeV using a sample of 19.3 +/- 0.7 pb(-1) accumulated by the Collider Detector at Fermilab. The cross section is measured in the central rapidity region \y\ < 1 for p(T)(B) > 6.0 GeV/c by fully reconstructing the B meson decays B+ --> J/psi K+ and B-0 --> J/psi K-*0(899), where J/psi --> mu(+)mu(-) and K-*0 --> K(+)pi(-). A comparison is made to the theoretical QCD prediction calculated at next-to-leading order. RI Vucinic, Dejan/C-2406-2008; Chiarelli, Giorgio/E-8953-2012; Azzi, Patrizia/H-5404-2012