  The possibility of radiative gauge symmetry breaking on D3-branes at
non-supersymmetric orbifold singularities is examined. As an example, a simple
model of D3-branes at non-supersymmetric C^3/Z_6 singularity with some
D7-branes for the cancellations of R-R tadpoles in twisted sectors is analyzed
in detail. We find that there are no tachyon modes in twisted sectors, and
NS-NS tadpoles in twisted sectors are canceled out, though uncanceled tadpoles
and tachyon modes exist in untwisted sectors. This means that this singularity
background is a stable solution of string theory at tree level, though some
specific compactification of six-dimensional space should be considered for a
consistent untwisted sector. On D3-brane three massless "Higgs doublet fields"
and three family "up-type quarks" are realized at tree level. Other fermion
fields, "down-type quarks" and "leptons", can be realized as massless modes of
the open strings stretching between D3-branes and D7-branes. The Higgs doublet
fields have Yukawa couplings with up-type quarks, and they also have
self-couplings which give a scalar potential without flat directions. Since
there is no supersymmetry, the radiative corrections may naturally develop
negative Higgs mass squared and "electroweak symmetry breaking". We explicitly
calculate the open string one-loop correction to the Higgs mass squared from
twisted sectors, and find that the negative value is indeed realized in this
specific model.
