Environmental issues are growing in importance due to waste management and depletion of fossil resources. Although modern society is largely based on polymeric materials, it is necessary to think about a more sustainable circular economy by developing new materials from renewable resources with sustainable end-of-life, which can help reducing the environmental impact of plastic wastes. Poly(3-hydroxybutyrate-co-3-hydroxyhexanoate) is a bio-based and biodegradable aliphatic polyester synthesized by bacteria, whose thermal and mechanical properties were enhanced by melt-compounding with acetylated cellulose nanocrystals (CNCs) at increasing concentrations from 5 up to 20 wt%. The obtained biocomposites were further extruded to obtain a constant filament used with a Fused Filament Fabrication (FFF) 3D printer. It was demonstrated that the bio-based composites are printable and different designs were realized: simple grid shapes, samples for characterization of rheological and thermo-mechanical properties, and also more complex architectures with vertical development and axis inclination. This work demonstrated the 3D printability of this new material and the results showed also improved thermal stability and thermomechanical properties of the composites, these findings were attributed to the optimized affinity between the biodegradable PHBH matrix and the functionalized CNCs. Furthermore, the results of this research showed that CNCs also offer a way to tailor the degree of disintegration of the composite materials, in line with the nanocellulose content. This novel grade of printable materials opens great opportunities for creating bio-based and biodegradable objects, combining the advantages of eco-friendly materials with the advantages of additive manufacturing. Particularly promising could be the application in a field where the high level of customization is an added value, such as in the field of biomedical engineering, for creating customized medical devices.