The linear MHD stability problem for 3D plasmas with noninteracting hot electron layers and nested magnetic flux surfaces in the absence of dissipation mechanisms is formulated in variational form. Boozer magnetic coordinates are extended to anisotropic pressure plasmas with nested magnetic flux surfaces for this purpose. A modified energy principle in which the hot electron species current is imperturbable is considered. Plasma incompressibility is imposed and thus a simplified kinetic energy is employed to determine the conditions of marginal stability. The vacuum region surrounding the plasma is treated as a shearless. pressureless and massless pseudoplasma. Fourier decomposition of the perturbations in the periodic angular variables of the magnetic coordinates is applied and a finite element discretization scheme reduces the stability problem to a special block pentadiagonal matrix eigenvalue equation which is amenable to solution with an inverse vector iteration technique. The formulation described is useful to evaluate the linear MHD stability properties of 3D plasma configurations with rigid hot electrons to global internal and external modes.