If the gauge fields of the standard model propagate in TeV-size extra dimen
sions, they rapidly become strongly coupled and can form scalar bound state
s of quarks and leptons. If the quarks and leptons of the third generation
propagate in 6 or 8 dimensions, we argue that the most tightly bound scalar
is a composite of top quarks, having the quantum numbers of the Higgs doub
let and a large coupling to the top quark. In the case where the gauge boso
ns propagate in a bulk of a certain volume, this composite Higgs doublet ca
n successfully trigger electroweak symmetry breaking. The mass of the top q
uark is correctly predicted to within 20%, without the need to add a fundam
ental Yukawa interaction, and the Higgs boson mass is predicted to lie in t
he range 165-230 GeV. In addition to the Higgs boson, there may be a few ot
her scalar composites sufficiently light to be observed at upcoming collide
r experiments.