Machine Learning (ML) in low-data settings remains an underappreciated yet crucial problem. This challenge is pronounced in low-to-middle income countries where access to large datasets is often limited or even absent. Hence, data augmentation methods to increase the sample size of datasets needed for ML are key to unlocking the transformative potential of ML in data-deprived regions and domains. Unfortunately, the limited training set constrains traditional tabular synthetic data generators in their ability to generate a large and diverse augmented dataset needed for ML tasks. To address this technical challenge, we introduce CLLM, which leverages the prior knowledge of Large Language Models (LLMs) for data augmentation in the low-data regime. While diverse, not all the data generated by LLMs will help increase utility for a downstream task, as for any generative model. Consequently, we introduce a principled curation process, leveraging learning dynamics, coupled with confidence and uncertainty metrics, to obtain a high-quality dataset. Empirically, on multiple real-world datasets, we demonstrate the superior performance of LLMs in the low-data regime compared to conventional generators. We further show our curation mechanism improves the downstream performance for all generators, including LLMs. Additionally, we provide insights and understanding into the LLM generation and curation mechanism, shedding light on the features that enable them to output high-quality augmented datasets. CLLM paves the way for wider usage of ML in data scarce domains and regions, by allying the strengths of LLMs with a robust data-centric approach.