Radio frequency cavities are among the most challenging and costly components of an accelerator facility. They are usually manufactured in individual parts, which are then joined by complex processes, e.g., several brazing steps. 3D printing has become an alternative to these conventional manufacturing methods due to higher cost efficiency, freedom in design, and recent achievement of high print quality for pure copper. A fully functional 3 GHz drift tube linac (DTL) prototype was 3D printed in one piece, made from pure copper by selective laser melting (SLM). To achieve a higher surface quality, the DTL geometry was optimized for the SLM process. The DTL design is related to the design of the DTL part of the side-coupled DTL modules used in linac-based proton therapy facilities. The quality factor (8750) and the shunt impedance per unit length (102mΩm) of the printed prototype are already comparable to traditionally manufactured DTL structures and can be further enhanced by surface treatments.