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In this article, we investigate the existence of a nontrivial solution for the nonlinear Choquard equation with upper critical exponent see Equation (6). The Riesz potential in this case has never been studied. We establish the existence of the ground state solution within bounded domains <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="sans-serif">Ω</mi><mo>⊂</mo><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mrow><mi>N</mi></mrow></msup></mrow></semantics></math></inline-formula>. Variational methods are used for this purpose. This method proved to be instrumental in our research, enabling us to address the problem effectively. The study of the existence of ground state solutions for the Choquard equation with a critical exponent has applications and relevance in various fields, primarily in theoretical physics and mathematical analysis.