  A global fit to the recent B->K*mu+mu- data shows indications for a large
new-physics contribution to the Wilson coefficient of the semi-leptonic vector
operator. In this article we consider a simple Z'-boson model of 3-3-1 type
that can accommodate such an effect without violating any other constraint from
quark-flavour physics. Implications for yet unobserved decay modes such as
B->Xsnunubar and longstanding puzzles like B->piK are also discussed. The
Z'-boson masses required to address the observed anomaly lie in the range of 7
TeV. Such heavy Z' bosons evade the existing bounds from precision data and
direct searches, and will remain difficult to discover even at a
high-luminosity LHC. The potential of an ILC as well as the next generation of
low-energy parity-violation experiments in constraining the Z'-boson parameter
space is also examined.
