Workload traces are essential to understand complex computer systems' behavior and manage processing and memory resources.Since real-world traces are hard to obtain, synthetic trace generation is a promising alternative.This paper proposes a first-of-a-kind approach that relies on training a large language model (LLM) to generate synthetic workload traces, specifically microservice call graphs.To capture complex and arbitrary hierarchical structures and implicit constraints in such traces, we propose to train LLMs to generate recursively, making call graph generation a sequence of more manageable steps.To further enforce learning constraints on the traces and generate uncommon situations, we apply additional instruction tuning steps to align our model with the desired trace features.With this method, we train TraceLLM, an LLM for microservice trace generation, and demonstrate that it produces diverse, realistic traces under varied conditions, outperforming existing approaches in both accuracy and validity.The synthetically generated traces can effectively replace real data to optimize important microservice management tasks.Additionally, TraceLLM adapts to downstream trace-related tasks, such as predicting key trace features and infilling missing data.