Continuous developments in additive manufacturing (AM) technology are opening up opportunities in novel machining, and improving design alternatives for modern particle accelerator components. One of the most critical, complex, and delicate accelerator elements to manufacture and assemble is the radio frequency quadrupole (RFQ) linear accelerator, which is used as an injector for all large modern proton and ion accelerator systems. For this reason, the RFQ has been selected by a wide European collaboration participating in the AM developments of the I.FAST (Innovation Fostering in Accelerator Science and Technology) Horizon 2020 project. The RFQ is as an excellent candidate to show how sophisticated pure copper accelerator components can be manufactured by AM and how their functionalities can be boosted by this evolving technology. To show the feasibility of the AM process, a prototype RFQ section has been designed, corresponding to one-quarter of a 750 MHz 4-vane RFQ, which was optimised for production with state-of-the-art laser powder bed fusion (L-PBF) technology, and then manufactured in pure copper. To the best of the authors’ knowledge, this is the first RFQ section manufactured in the world by AM. Subsequently, geometrical precision and surface roughness of the prototype were measured. The results obtained are encouraging and confirm the feasibility of AM manufactured high-tech accelerator components. It has been also confirmed that the RFQ geometry, particularly the critical electrode modulation and the complex cooling channels, can be successfully realised thanks to the opportunities provided by the AM technology. Further prototypes will aim to improve surface roughness and to test vacuum properties. In parallel, laboratory measurements will start to test and improve the voltage holding properties of AM manufactured electrode samples.