  This is the first of at least two articles that describe the moduli spaces of
pseudoholomorphic, multiply punctured spheres in R x (S^1 x S^2) as defined by
a certain natural pair of almost complex structure and symplectic form. This
article proves that all moduli space components are smooth manifolds. Necessary
and sufficient conditions are also given for a collection of closed curves in
S^1 x S^2 to appear as the set of |s| --> infinity limits of the constant s in
R slices of a pseudoholomorphic, multiply punctured sphere.
