Effort estimation is a crucial activity in agile software development, where teams collaboratively review, discuss, and estimate the effort required to complete user stories in a product backlog. Current practices in agile effort estimation heavily rely on subjective assessments, leading to inaccuracies and inconsistencies in the estimates. While recent machine learning-based methods show promising accuracy, they cannot explain or justify their estimates and lack the capability to interact with human team members. Our paper fills this significant gap by leveraging the powerful capabilities of Large Language Models (LLMs). We propose a novel LLM-based multi-agent framework for agile estimation that not only can produce estimates, but also can coordinate, communicate and discuss with human developers and other agents to reach a consensus. Evaluation results on a real-life dataset show that our approach outperforms state-of-the-art techniques across all evaluation metrics in the majority of the cases. Our human study with software development practitioners also demonstrates an overwhelmingly positive experience in collaborating with our agents in agile effort estimation.