  We study polar molecules in a stack of strongly confined pancake traps. When
dipolar moments point perpendicular to the planes of the traps and are
sufficiently strong, the system is stable against collapse but attractive
interaction between molecules in different layers leads to the formation of
extended chains of molecules, analogously to the chaining phenomenon in
classical rheological electro- and magnetofluids. We analyze properties of the
resulting quantum liquid of dipolar chains and show that only the longest
chains undergo Bose-Einstein condensation with a strongly reduced condensation
temperature. We discuss several experimental methods for studying chains of
dipolar molecules.
