Large Language Models (LLMs) are currently pre-trained and fine-tuned on large cloud servers. The next frontier is LLM personalization, where a foundation model can be fine-tuned with user/task-specific data. Given the sensitive nature of such private data, it is desirable to fine-tune these models on edge devices to improve user trust. However, fine-tuning on resource-constrained edge devices presents significant challenges due to substantial memory and computational demands, as well as limited infrastructure support. We observe that inference engines (e.g., ExecuTorch) can be repurposed for fine-tuning by leveraging zeroth-order (ZO) optimization, which uses multiple forward passes to approximate gradients. While promising, direct application of ZO methods on edge devices is inefficient due to the high computational cost of multiple forward passes required for accurate gradient estimation, and their deployment has been largely unexplored in practice. We introduce MobiZO, a resource-efficient fine-tuning framework for LLMs specifically designed for edge devices. MobiZO combines three key innovations: (1) a parallelized randomized gradient estimator that employs both outer-loop and inner-loop parallelism to eliminate sequential forward passes, (2) a specialized Multi-Perturbed LoRA (MP-LoRA) module that enables efficient realization of both inner and outer loop parallelism, and (3) a seamless integration with ExecuTorch for on-device training, requiring no modifications to the runtime. Experiments demonstrate that MobiZO achieves substantial runtime speedups and memory savings while improving fine-tuning accuracy, paving the way for practical deployment of LLMs in real-time, on-device applications. Code available at: \url{anonymous.4open.science/r/MobiZO-DBC6}.