  We study genus 3 hyperelliptic curves which have an extra involution. The
locus $\L_3$ of these curves is a 3-dimensional subvariety in the genus 3
hyperelliptic moduli $\H_3$. We find a birational parametrization of this locus
by affine 3-space. For every moduli point $\p \in \H_3$ such that $|\Aut
(\p)|>2$, the field of moduli is a field of definition. We provide a rational
model of the curve over its field of moduli for all moduli points $\p \in \H_3$
such that $|\Aut(\p)|>4$. This is the first time that such a rational model of
these curves appears in the literature.
