Historically, large physics problems have been divided into smaller problems based on the individual physics, typically referred to as operator splitting. The analysis of a nuclear reactor for design-basis accidents is performed by a handful of computer codes each solving a portion of the problem, based on the physics involved. The reactor thermal-hydraulic response to an event is determined using a system code like TRAC RELAP Advanced Computational Engine (TRACE). The core power response to the same accident scenario is determined using a spatial neutron kinetics code like Purdue Advanced Reactor Core Simulator (PARCS). The drive of industry to uprate power for reactors has motivated analysts to move from a conservative approach to design-basis accidents toward a best-estimate method. To achieve a best-estimate calculation, efforts have been aimed at coupling the individual physics models to improve the accuracy of the analysis and reduce margins. The current coupling techniques are sequential in nature (i.e., they treat shared data explicitly in time). During a calculation time-step data are passed between the two codes. The individual codes solve their portions of the calculation and converge to a solution before the calculation is allowed to proceed to the next time step. This paper presents a fully implicit method of simultaneously solving the neutron balance equations, heat conduction equations, and constitutive fluid dynamics equations. The paper also outlines the basic concepts behind the nodal balance equations, heat transfer equations, and thermal-hydraulic equations, which will be coupled to form a fully implicit nonlinear system of equations. It presents a monolithic method for the solution of the implicit equation set. The coupling technique described in this paper was implemented into the TRACE/PARCS coupled code system and is applicable to other similar coupled thermal-hydraulic and core physics reactor safety codes. This technique is demonstrated using coupled input decks to show that the system is solved correctly and then verified by using simple one-dimensional coupled problems. These simplified problems demonstrate the ability of this method to solve nonlinear coupled systems and maintain accuracy while removing time-step dependency of the coupled calculation.