We propose a simple statistical mechanical theory for a strongly dipolar fluid at low densities, based on the analogy between a polymer chain and a chain formed by strongly polar particles. The general methods developed in the theory of semiflexible polymers enable one to obtain simple expressions for the energy and conformational entropy of a long dipole chain. We then consider the equilibrium between chains of different lengths and derive a general expression for the free energy as a functional of the chain length distribution. Both steric and dipolar interactions between long chains are shown to be weak and as a result the rarefied fluid of strongly dipolar spheres resembles the ideal gas of noninteracting polydisperse chains. It is shown that the chain length distributions found in simulations are compatible with the assumption of very weak interchain interactions if strong finite-size effects are taken into account. We also investigate whether sufficiently strong attractive van der Waals forces between particles can cause dissociation of the chains. Finally, we discuss the case of a dipolar fluid in an applied field and argue that the coexistence between two aligned phases of chains, as observed by computer simulation, is unlikely to occur in an infinite system.