Using polymer physics theory, we calculate the free energy difference of a single dipolar hard sphere chain and that of a dipolar fluid without chain structure at low density. The condition for the formation of a single dipolar chain is derived. A dipolar chain will be formed only when the dipole moment is stronger than a threshold value. For a dipolar chain consisting of N dipoles, the total dipole moment distribution is calculated to be a Gaussian function with finite-N correction. For a system consisting of many monodisperse dipolar chains, mean field calculations show that a phase transition occurs for sufficiently strong dipole strength or low enough temperature. The spontaneous polarization of the system and the critical dipole strength are also obtained. Furthermore, the chain length distribution function is obtained by the variational method.
