A search for the X(4140) state in B+ -> J/psi phi K+ decays is performed with 0.37 fb(-1) of pp collisions at root s = 7 TeV collected by the LHCb experiment. No evidence for this state is found, in 2.4 sigma disagreement with a measurement by CDF. An upper limit on its production rate is set, B(B+ -> X(4140)K+) x B(X(4140) -> J/psi phi)/B(B+ -> J/psi phi K+) < 0.07 at 90% confidence level.