  We present the first evidence from lattice simulations that the magnetic
monopoles in three dimensional compact quantum electrodynamics (cQED3) with
N_f=2 and N_f= 4 four-component fermion flavors are in a plasma phase. The
evidence is based mainly on the divergence of the monopole susceptibility
(polarizability) with the lattice size at weak gauge couplings. A weak
four-Fermi term added to the cQED3 action enabled simulations with massless
fermions. The exact chiral symmetry of the interaction terms forbids symmetry
breaking lattice discretization counterterms to appear in the theory's
effective action. It is also shown that the scenario of a monopole plasma does
not depend on the strength of the four-Fermi coupling. Other observables such
as the densities of "isolated" dipoles and monopoles and the so-called specific
heat show that a crossover from a dense monopole plasma to a dilute monopole
gas occurs at strong couplings. The implications of our results on the
stability of U(1) spin liquids in two spatial dimensions are also discussed.
