A new method for calculating the partition function of real gases is developed and applied to a system of point charges without repulsive core, e.g., a fully ionized hydrogen gas. The electrostatic energy U of the total system is represented as a function of the Fourier coefficients, A s, of the particle density, and the configuration integral is evaluated by direct integration in the function space which is generated by the A s. To this purpose, the A s are treated as stochastic variables characterized by a multivariate probability density whose determination represents a major part of this paper. The potential of mean force, W( r) is found equal to the average Debye-Hückel potential, ( Z 2e 2 r ) exp ( −r h ), ( Ze = ionic charge, h = Debye shielding length). The radial distribution function g( r) is determined as g(r) = exp[ −W(r) kT ] , and the part of U which is proportional to the total particle number N is found to be equal to the Debye-Hückel energy.