We use cosmic microwave background data from WMAP, ACBAR, VSA and CBI, and galaxy power spectrum data from 2dF, to constrain flat cosmologies based on the Jordan-Brans-Dicke theory, using a Markov Chain Monte Carlo approach. Using a parametrization based on xi=1/4omega, and performing an exploration in the range lnxi in [-9,3], we obtain a 95% marginalized probability bound of lnxi < -6.2, corresponding to a 95% marginalized probability lower bound on the Brans-Dicke parameter omega>120.