The existence of a class of nontopological ``string'' soliton solutions is demonstrated. The string consists of a long, thin region of false vacuum supported against collapse by the pressure of massless particles trapped in its interior. It is shown that the string configuration is stable against decay into free particles. The stability of such ``strings'' to arbitrary small perturbations is analyzed and the solutions are shown to be unstable to the migration of charge along the string, leading to a conversion of the nontopological string into spherical nontopological solitons.