  Spiral waves are investigated in chemical systems whose underlying
spatially-homogeneous dynamics is governed by a deterministic chaotic
attractor. We show how the local periodic behavior in the vicinity of a spiral
defect is transformed to chaotic dynamics far from the defect. The
transformation occurs by a type of period doubling as the distance from the
defect increases. The change in character of the dynamics is described in terms
of the phase space flow on closed curves surrounding the defect.
