Language modeling has witnessed remarkable advancements in recent years, with Large Language Models (LLMs) like ChatGPT setting unparalleled benchmarks in human-like text generation. However, a prevailing limitation is the underrepresentation of languages like Tamil in these cutting-edge models, leading to suboptimal performance in diverse linguistic contexts. This paper addresses this lacuna, enhancing the open-source LLaMA model with an addition of 16,000 Tamil tokens, aiming to achieve superior text generation and comprehension in the Tamil language. We strategically employ the LoRA methodology for efficient model training on a comprehensive Tamil corpus, ensuring computational feasibility and model robustness. Moreover, we introduce a Tamil-translated version of the Alpaca dataset and a subset of the OpenOrca dataset tailored for instruction fine-tuning. Our results showcase significant performance improvements in Tamil text generation, with potential implications for the broader landscape of LLMs in Indian languages. We further underscore our commitment to open research by making our models, datasets, and code publicly accessible, fostering further innovations in language modeling.