Generative Artificial Intelligence (AI) promises to make a vast impact across disciplines, including transforming the architectural design process by autonomously generating full building geometries. One form of generative deep learning that has been used to create 2D and 3D representations of objects is Generative Adversarial Networks (GANs). Existing literature, however, has limited applications that utilize 3D data for building geometry generation, with previous studies focused on low-scale 3D geometries suitable for objects such as chairs or cars. The thesis identifies and modifies a training data set and then develops a new GAN architecture to produce high-resolution feasible building geometry. The training dataset used is a selection of 3D models of single-family homes from an existing database, pre-processed for the specific application. State-of-the-art GAN models are initially tested to establish baseline performance and applicability potential. Then, a systematic study is performed to identify the structure and hyperparameters necessary to successfully fit a GAN to this design task. The successful architecture, named 3DBuildingGAN, uses a combination of Wasserstein loss with gradient penalty, leaky rectified linear units for neuron activation in the generator and the critic, and the root mean squared propagation optimizer with a fixed learning rate. The proposed model generates outputs similar in size, shape, and proportion to the training data with minimal noise in the output. Evaluation of memorization properties indicates open research directions, such as incorporating memorization rejection and training on larger data sets.