  We describe convex hulls of the simplest compact space curves, reducible
quartics consisting of two circles. When the circles do not meet in complex
projective space, their algebraic boundary contains an irrational ruled surface
of degree eight whose ruling forms a genus one curve. We classify which curves
arise, classify the face lattices of the convex hulls, and determine which are
spectrahedra. We also discuss an approach to these convex hulls using
projective duality.
