The emergence of the large language model (LLM) poses an exponential growth of demand for computation throughput, memory capacity, and communication bandwidth. Such a demand growth has significantly surpassed the improvement of corresponding chip designs. With the advancement of fabrication and integration technologies, designers have been developing Wafer-Scale Chips (WSCs) to scale up and exploit the limits of computation density, memory capacity, and communication bandwidth at the level of a single chip. Existing solutions have demonstrated the significant advantages of WSCs over traditional designs, showing potential to effectively support LLM workloads. Despite the benefits, exploring the early-stage design space of WSCs for LLMs is a crucial yet challenging task due to the enormous and complicated design space, time-consuming evaluation methods, and inefficient exploration strategies. To address these challenges, we propose Theseus, an efficient WSC design space exploration framework for LLMs. We construct the design space of WSCs with various constraints considering the unique characteristics of WSCs. We propose efficient evaluation methodologies for large-scale NoC-based WSCs and introduce multi-fidelity Bayesian optimization to efficiently explore the design space. Evaluation results demonstrate the efficiency of Theseus that the searched Pareto optimal results outperform GPU cluster and existing WSC designs by up to 62.8%/73.7% in performance (with the same or lower power) and 38.6%/42.4% in power consumption (with the same or higher performance) for LLM training, while improving up to 23.2× and 15.7× for the performance and power of inference tasks. Furthermore, we conduct case studies to address the design tradeoffs in WSCs and provide insights to facilitate WSC designs for LLMs.