We present a measurement of the Hall coefficient RH for an untwinned single crystal of YBa2Cu3O7-x. The crystal was produced by a method that does not involve thermomechanical detwinning, and has a resistivity among the copper-oxide chains of only 29-mu-OMEGA-cm at 100 K, indicating high sample quality. The in-plane resistivity and 1/R(H) become linear in temperature as T rises significantly above T(c). Near T(c) we observe deviation from this linearity, and we interpret it as indicating thermodynamic fluctuations in a layered superconductor. Fits of this model to both the resistivity and Hall-effect data yield physically reasonable values for the fitting parameters. Evidence is obtained that the two copper-oxide planes in each unit cell are tightly coupled, acting as one superconducting layer. Surprisingly, the best fits indicate that the Hall-effect fluctuations are dominated by the Maki-Thompson process rather than the Aslamazov-Larkin process.