  The contraction of the image of the Johnson homomorphism is called the
Chillingworth class. In this paper, we derive a combinatorial description of
the Chillingworth class for Putman's subsurface Torelli groups. We also prove
the naturality and uniqueness properties of the map whose image is the dual of
the Chillingworth classes of the subsurface Torelli groups. Moreover, we relate
the Chillingworth class of the subsurface Torelli group to the partitioned
Johnson homomorphism.
