  We study ballistic electron transport through a finite chain of quantum
circular rings in the presence of spin-orbit interaction of strength \alpha.
For a single ring the transmission and reflection coefficients are obtained
analytically and from them the conductance for a chain of rings as a function
of \alpha and of the wave vector k of the incident electron. We show that due
to destructive spin interferences the chain can be totaly opaque for certain
ranges of k the width of which depends on the value of \alpha. A periodic
modulation of the strength \alpha or of the ring radius widens up the gaps
considerably and produces a nearly binary conductance output.
