  We propose a new spontaneous supersymmetry breaking mechanism, in which extra
compact dimensions play an important role. To illustrate our mechanism, we
study a simple model consisting of two chiral superfields, where one spatial
dimension is compactified on a circle $S^1$. It is shown that supersymmetry is
spontaneously broken irrespective of the radius of the circle, and also that
the translational invariance for the $S^1$-direction and a global symmetry are
spontaneously broken when the radius becomes larger than a critical radius.
These results are expected to be general features of our mechanism. We further
discuss that our mechanism may be observed as the O'Raifeartaigh type of
supersymmetry breaking at low energies.
