  We study properties of quantum chains in a gas of polar bosonic molecules
confined in a stack of N identical one- and two- dimensional optical lattice
layers, with molecular dipole moments aligned perpendicularly to the layers.
Quantum Monte Carlo simulations of a single chain (formed by a single molecule
on each layer) reveal its quantum roughening transition. The case of finite
in-layer density of molecules is studied within the framework of the J-current
model approximation, and it is found that N-independent molecular superfluid
phase can undergo a quantum phase transition to a rough chain superfluid. A
theorem is proven that no superfluidity of chains with length shorter than N is
possible. The scheme for detecting chain formation is proposed.
