We consider inflation driven by the energy density of a conventional scalar field minimally coupled to gravity, which has an initial vacuum expectation value which is large compared with the value at the minimum of its potential ("chaotic inflation"), in the context of Brans-Dicke-type models with a time-dependent Newton's constant. The equations of motion for the scalar field driving inflation and the Brans-Dicke scalar are solved in the slow-rolling approximation for the case of a lambda-sigma-4 potential driving inflation, and the magnitude and spectrum of density perturbations produced during inflation are calculated. Sufficient inflation to account for the observed homogeneity and isotropy of the Universe is found to occur only if the coupling epsilon between the Brans-Dicke scalar and the Ricci scalar is smaller than 1. It is shown that only in the case where the initial value of the scalar field driving inflation is large compared with the initial value of the Brans-Dicke scalar can epsilon be larger than 10(-3), and that in this case the self-coupling lambda is constrained to be much smaller than in the case of conventional chaotic inflation models. It is shown also that the spectrum of density perturbations is sufficiently flat to explain galaxy formation only if epsilon <0.04.