A theory of a confined two-dimensional electrolyte is presented. The positi
ve and negative ions, interacting by a l/r potential, are constrained to mo
ve on an interface separating two solvents with dielectric constants epsilo
n (1) and epsilon (2). It is shown that the Debye-Huckel type of theory pre
dicts that this two-dimensional Coulomb fluid should undergo a phase separa
tion into a coexisting liquid (high-density) and gas (low-density) phases.
We argue, however, that the formation of polymerlike chains of alternating
positive and negative ions can prevent this phase transition from taking pl
ace.