The general trace reconstruction problem seeks to recover an original sequence from its noisy copies independently corrupted by insertions, deletions, and substitutions. This problem arises in applications such as DNA data storage, a promising storage medium due to its high information density and longevity. However, errors introduced during DNA synthesis, storage, and sequencing require correction through algorithms and codes, with trace reconstruction often used as part of data retrieval. In this work, we propose TReconLM, a decoder-only transformer that solves trace reconstruction as a next-token prediction task. TReconLM outperforms state-of-the-art trace reconstruction algorithms, including prior deep-learning approaches, recovering a substantially higher fraction of sequences without error. We pretrain on synthetic data generated from a simple error model and fine-tune on real-world data to adapt to technology-specific error patterns. Code is available at https://github.com/MLI-lab/TReconLM.