A novel autonomous chunk-based aerial additive manufacturing framework is presented, supported with experimental demonstration advancing aerial 3D printing. An optimization-based decomposition algorithm transforms structures into sub-components, or chunks, treated as individual tasks coordinated via a dependency graph, ensuring sequential assignment to UAVs considering inter-dependencies and printability constraints for seamless execution. A specially designed hexacopter equipped with a pressurized canister for lightweight expandable foam extrusion is utilized to deposit the material in a controlled manner. To further enhance precise execution of the printing, an offset-free Model Predictive Control mechanism is considered compensating reactively for disturbances and ground effect during execution. Additionally, an interlocking mechanism is introduced in the chunking process to enhance structural cohesion and improve layer adhesion. Extensive experiments demonstrate the framework's effectiveness in constructing precise structures of various shapes while seamlessly adapting to practical challenges, proving its potential for a transformative leap in aerial robotic capability for autonomous construction.