  We construct an infinite number of Shimura curves contained in the locus of
hyperelliptic Jacobians of genus 3. In the opposite direction, we show that in
genus 3 the only possible non-complete (in the moduli space of abelian
threefolds) Kuga curves contained in the hyperelliptic locus have the same
degeneration data as that of the examples we construct.
  The locus of genus 3 hyperelliptic Jacobians is a divisor within the moduli
space of principally polarized abelian threefolds, and our result demonstrates
the techniques we develop more generally for dealing with Shimura curves
contained within a divisor in the moduli space of abelian varieties.
