  We construct domain walls and instantons in a class of models with coupled
scalar fields, determining, in agreement with previous studies, that many such
solutions contain naked timelike singularities. Vacuum bubble solutions of this
type do not contain a region of true vacuum, obstructing the ability of eternal
inflation to populate other vacua. We determine a criterion that potentials
must satisfy to avoid the existence of such singularities, and show that many
domain wall solutions in Type IIB string theory are singular. This has profound
implications for applying the program of eternal inflation to making
predictions in the string theory landscape.
