The aim of this work is to investigate the formation of an anomalously high fraction of twin boundaries (TBs) during laser directed energy deposition (DED) of a Mg-3Al-1 Zn (wt.%) alloy. With that goal, single tracks are deposited using different combinations of scan speed and powder feed rate. The melt pool dimensions are related to the DED parameters. Irrespective of the processing conditions, the resulting microstructures are always formed by fine grains with a very weak texture. However, some DED parameter combinations give rise to a fraction of TBs that is significantly higher than that corresponding to a random texture. These TBs are characterized by an irregular morphology and by the presence of segregated atoms, solute clusters, and nanoparticles. Additionally, the lattice in the vicinity of the TBs is highly distorted and contains a high population of stacking faults. All these characteristics set them apart from conventional tensile TBs, which exhibit a large degree of coherency and limited segregation. Rapid solidification is thus presented here as a novel avenue to design TBs with unique properties in Mg alloys. This work paves the way for future studies on grain boundary design via additive manufacturing methods, a field that is still in its infancy.