Advanced aluminides strengthened with incoherent Laves phase precipitates are promising lightweight and creep-resistant alternatives for high-alloy steels and superalloys for high-temperature critical components up to 750 °C service temperature. A significant issue with manufacturing these aluminides with conventional casting is the strong coarsening tendency of the Laves phase precipitates at elevated temperatures, leading to a significant strength reduction. In this context, the short lifetime of the melt pool in additive manufacturing and its fast solidification and cooling rates promise to consolidate these aluminides with homogeneously distributed fine Laves phase particles without coarsening. The main scientific objective of this work is to exploit the unique characteristics of the laser powder bed fusion (L-PBF) additive manufacturing (AM) process to print dense and crack-free bulk Fe3Al-1.5Ta samples containing uniformly distributed (Fe, Al)2Ta Laves phase precipitates. The Fe-25Al-2Ta (at.%) alloy was selected for this work since its creep resistance at 650 °C surpasses the one of the P92 martensitic–ferritic steel (one of the most creep-resistant alloys developed for steam turbine applications). Fundamentals on process–microstructure relationships governing the L-PBF-fabricated builds are provided by a detailed microstructural characterization using X-ray diffractometer (XRD) and ultra-high-resolution scanning electron microscopy (SEM) equipped with energy-dispersive X-ray spectroscopy (EDX) and high-resolution electron backscatter diffraction (EBSD) detectors. Orientation imaging microscopy (OIM) and grain reference orientation deviation (GROD) maps were applied to measure texture and visualize substructures within the grains. The mechanism of voids formation, morphology, and volume fraction as a function of the input energy density was identified. The melting and solidification dynamics led to microstructures with large columnar grains, porosity, and periodic cracks during the printing process. Processing samples at the building temperatures below the brittle-to-ductile transition temperature, BDTT (750 °C), often caused severe macrocracking and delamination. Crack-free samples with densities higher than 99%, some approaching 99.5%, were fabricated from pre-alloyed gas-atomized powders with a combination of high laser power (250–300 W), slow-to-medium scanning speed (500–1000 mm/s), and 800 °C build plate preheating using a 67° rotation scanning strategy. The morphology of the pores in the volume of the samples indicated a relatively sharp transition from spherical geometry for scanning speeds up to 1000 mm/s to crack-like pores for higher values. The ultra-fast cooling during the L-PBF process suppressed D03 Fe3Al-ordering. The Fe3Al-1.5Ta builds were characterized by B2 FeAl-type order clusters dispersed within a disordered A2 α-(Fe, Al) matrix. Additionally, the (Fe, Al)2Ta Laves phase (C14–P63/mmc) was predominantly formed at the matrix phase grain boundaries and frequently dispersed within the grains. The quantitative EDX analysis of the matrix gave 77.6–77.9 at.% Fe, 21.4–21.7 at.% Al, and 0.6–0.8 at.% Ta, while the composition of the Laves phase was 66.3–67.8 at.% Fe, 8.7–9.8 at.% Al, and 22.4–24.9 at.% Ta, indicating that the Laves phase is considerably enriched in Ta with respect to the matrix. The L-PBF-fabricated alloys were characterized by coarse, columnar grains which grow epitaxially from the substrate, were several m in width, and extended across several layers along the building direction. The grains exhibited a relatively strong microtexture close to <0 0 1> with respect to the building direction. The L-PBF builds showed a bulk hardness value comparable to the as-cast and spark plasma-sintered counterparts. A negligible variation of the hardness across the build height was observed. Within the framework of this study, we demonstrated that the porosity and cracking issues could be resolved mainly by controlling the process parameters and preheating the build platform above the BDTT. Nevertheless, alloy modifications and/or post-manufacturing processing are required for microstructure refinement.