We analyze 9.7 x 10^6 B\bar{B}$ pairs recorded with the CLEO detector to determine the production ratio of charged to neutral B-meson pairs produced at the Y(4S) resonance. We measure the rates for B^0 -> J/psi K^{(*)0} and B^+ -> J/psi K^{(*)+} decays and use the world-average B-meson lifetime ratio to extract the relative widths f+-/f00 = Gamma(Y(4S) -> B+B-)/Gamma(Y(4S) -> B0\bar{B0}) = = 1.04 +/- 0.07(stat) +/- 0.04(syst). With the assumption that f+- + f00 = 1, we obtain f00 = 0.49 +/- 0.02(stat) +/- 0.01(syst) and f+- = 0.51 +/- 0.02(stat) +/- 0.01(syst). This production ratio and its uncertainty apply to all exclusive B-meson branching fractions measured at the Y(4S) resonance.