The 2H(e,e(')p)n cross section was measured in Hall A of the Thomas Jefferson National Accelerator Facility near the top of the quasielastic peak (x(Bj)=0.964) at a four-momentum transfer squared, Q(2)=0.665 (GeV/c) (2) (omega=0.368 GeV, W=2.057 GeV), and for recoil momenta up to 550 MeV/c. The measured cross section deviates by 1-2sigma from a state-of-the-art calculation at low recoil momenta. At high recoil momenta the cross section is well described by the same calculation; however, in this region, final-state interactions and interaction currents are predicted to be large, and alternative choices of nucleon-nucleon potential and nucleon current operator may result in significant spread in the calculations.