  We construct monopole-antimonopole chain and vortex solutions in
Yang-Mills-Higgs theory coupled to Einstein gravity. The solutions are static,
axially symmetric and asymptotically flat. They are characterized by two
integers (m,n) where m is related to the polar angle and n to the azimuthal
angle. Solutions with n=1 and n=2 correspond to chains of m monopoles and
antimonopoles. Here the Higgs field vanishes at m isolated points along the
symmetry axis. Larger values of n give rise to vortex solutions, where the
Higgs field vanishes on one or more rings, centered around the symmetry axis.
When gravity is coupled to the flat space solutions, a branch of gravitating
monopole-antimonopole chain or vortex solutions arises, and merges at a maximal
value of the coupling constant with a second branch of solutions. This upper
branch has no flat space limit. Instead in the limit of vanishing coupling
constant it either connects to a Bartnik-McKinnon or generalized
Bartnik-McKinnon solution, or, for m>4, n>4, it connects to a new
Einstein-Yang-Mills solution. In this latter case further branches of solutions
appear. For small values of the coupling constant on the upper branches, the
solutions correspond to composite systems, consisting of a scaled inner
Einstein-Yang-Mills solution and an outer Yang-Mills-Higgs solution.
