  We report on a search for the recently reported X(3872) state using 15.1
fb^{-1} e+ e- data taken in the \sqrt{s} = 9.46-11.30 GeV region. Separate
searches for the production of X(3872) in untagged gamma-gamma fusion and e+ e-
annihilation following initial state radiation (ISR) are made by taking
advantage of the unique correlation of J/psi -> l+ l- in X(3872) decay to pi+
pi- J/psi. No signals are observed in either case, and 90% confidence upper
limits are established as (2J+1)\Gamma_{\gamma\gamma}B(X -> pi+ pi- J/psi) <
12.9 eV and \Gamma_{ee}B(X -> pi+ pi- J/psi) < 8.3 eV.
