We examine the possibility of static wormhole solutions in the vacuum
Brans-Dicke theory both in the original (Jordan) frame and in the conf
ormally rescaled (Einstein) frame. It turns out that, in the former fr
ame, wormholes exist only in a very narrow interval of the coupling pa
rameter, viz., -3/2<omega<-4/3. It is shown that these wormholes are n
ot traversable in practice. In the latter frame, wormhole solutions do
not exist at all unless energy conditions are violated by hand.