The largest light-harvesting antenna in nature, the chlorosome, is a heterogeneous helical BChl self-assembly that has evolved in green bacteria to harvest light for performing photosynthesis in low-light environments. Guided by NMR chemical shifts and distance constraints for Chlorobaculum tepidum wild-type chlorosomes, the two contrasting packing modes for syn-anti parallel stacks of BChl c to form polar 2D arrays, with dipole moments adding up, are explored. Layered assemblies were optimized using local orbital density functional and plane wave pseudopotential methods. The packing mode with the lowest energy contains syn-anti and anti-syn H-bonding between stacks. It can accommodate R and S epimers, and side chain variability. For this packing, a match with the available EM data on the subunit axial repeat and optical data is obtained with multiple concentric cylinders for a rolling vector with the stacks running at an angle of 21° to the cylinder axis and with the BChl dipole moments running at an angle ~ 55° to the tube axis, in accordance with optical data. A packing mode involving alternating syn and anti parallel stacks that is at variance with EM appears higher in energy. A weak cross-peak at -6 ppm in the MAS NMR with 50 kHz spinning, assigned to C-181, matches the shift of antiparallel dimers, which possibly reflects a minor impurity-type fraction in the self-assembled BChl c.