Asymmetric two-dimensional (2D) structures (often named Janus), like SeMoS and their nanotubes, have tremendous scope in material chemistry, nanophotonics, and nanoelectronics due to a lack of inversion symmetry and time-reversal symmetry. The synthesis of these structures is fundamentally difficult owing to the entropy-driven randomized distribution of chalcogens. Indeed, no Janus nanotubes were experimentally prepared, so far. Serendipitously, a family of asymmetric misfit layer superstructures (tubes and flakes), including LaX-TaX2 (where X = S/Se), were synthesized by high-temperature chemical vapor transport reaction in which the Se binds exclusively to the Ta atoms and La binds to S atoms rather than the anticipated random distribution. With increasing Se concentration, the LaS-TaX2 misfit structure gradually transformed into a new LaS-TaSe2-TaSe2 superstructure. No misfit structures were found for xSe = 1. These counterintuitive results shed light on the chemical selectivity and stability of misfit compounds and 2D alloys, in general. The lack of inversion symmetry in these asymmetric compounds induces very large local electrical dipoles. The loss of inversion and time-reversal symmetries in the chiral nanotubes offers intriguing physical observations and applications.