  We study a quantum phase transition in a system of dipoles confined in a
stack of $N$ identical one-dimensional lattices (tubes) polarized
perpendicularly to the lattices. In this arrangement the intra-lattice
interaction is purely repulsive preventing the system collapse and the
inter-lattice one is attractive. The dipoles may represent polar molecules or
indirect excitons. The transition separates two phases; in one of them
superfluidity (understood as algebraic decay of the corresponding correlation
functions) takes place in each individual lattice, in the other (chain
superfluid) the order parameter is the product of bosonic operators from all
lattices. We argue that in the presence of finite inter-lattice tunneling the
transition belongs to the universality class of the $q=N$ two-dimensional
classical Potts model. For $N=2,3,4$ the corresponding low energy field theory
is the model of Z$_N$ parafermions perturbed by the thermal operator. Results
of Monte Carlo simulations are consistent with these predictions. The detection
scheme for the chain superfluid of indirect excitons is outlined.
