In situ alloying and fabricating glassy structures through a layer-by-layer fashion approach are challenging but have high potential to develop novel-graded materials. For the first time, this cost-effective approach is applied to additive manufacturing (AM) of a Zr-based bulk metallic glass (BMG) from high-entropy alloys (HEAs). A newly developed composition of Zr40Al20Cu20Ti20 is fabricated through laser powder bed fusion (LPBF). Process parameters are optimized within a wide range of laser power (50–200 W) as well as scanning speed (50–800 mm s−1). In all printed samples, microscopic and compositional examinations reveal no glass formation, but very fine grains and CuTi and AlTi nanocrystals. Some glassy transitions at the interfaces may be encouraged to occur with proper melting and mixing. However, the main reason for not obtaining a glassy matrix is the substantial proportion of unmelted Zr raw powder throughout the structure as spherical particles. Consequently, glass formation can be hindered by a considerable amount of compositional deviation. During LPBF, in situ alloying poses significant challenges to developing BMGs. Hence, the various stages of the process, including raw material specifications, laser settings, and process parameters, should be investigated further.