The field of polariton chemistry has excited the imagination of chemists, physicists, and materials scientists who have demonstrated many compelling ways that strong coupling between light and molecules can affect chemical properties and dynamics. The theoretical challenges in polaritonic chemistry bridge most domains of chemical physics, including ab initio quantum chemistry, cavity quantum electrodynamics, computational electrodynamics, statistical thermodynamics, and rate theories as pointed out by a recent review and perspective articles on theoretical advances in polaritonic chemistry. In this work, we introduce a method called Cavity Quantum Electrodynamics Complete Active Space Configuration Interaction theory (QED-CASCI) that provides a variational route to ground-and excited-state polariton states and assess its accuracy against several model systems for which we can provide numerically exact benchmarks. QED-CASCI provides an important theoretical toolkit at the intersection of ab initio quantum chemistry and cavity quantum electrodynamics, which we will generally refer to here as ab initio cavity quantum electrodynamics, that should be able to inherit many of the favorable properties that have enabled CASCI to become a workhorse method in simulating ab initio molecular dynamics on multiple potential energy surfaces, namely smooth potential energy surfaces, size consistent and size intensive vertical excitation energies, the ability to formulate analytic nuclear derivatives and derivative couplings, and the ability to formulate relatively simple corrections to incorporate dynamic correlation. The goal of ab initio cavity quantum electrodynamics methodologies, in general, is to provide a detailed and rigorous description of the molecular energy eigenstates coupled to quantized photon states that are treated within the framework of cavity quantum electrodynamics. Ideally, these approaches should provide reliable accuracy across coupling regimes, i.e. spanning weak, strong, and ultra-strong coupling. There are at least two complementary approaches to this problem: so-called parameterized CQED methods and self-consistent CQED methods. The former parameterized approach involves solving two Schrödinger equations in series: a first for the molecular system alone using traditional tools of ab initio quantum chemistry, and the second for the coupled molecularphotonic system that is parameterized by the solutions to the molecular problem. On the other hand, the self-consistent approach involves augmenting ab initio quantum chemistry methods to directly include coupling to photonic degrees of freedom. Such approaches have included quantum electrodynamics generalizations of density functional theory (QEDFT and QED-DFT ), real-time and linear-response formulations of QED-TDDFT, configuration interaction (QED-CIS), cavity QED extension of second-order Møller-Plesset perturbation theory and the algebraic diagrammatic construction, coupled cluster (QED-CC), variational QED-2-RDM methods, and diffusion Monte Carlo. To the best of our knowledge, this is the first formulation of QED-CASCI.