The classical easy-plane antiferromagnetic chain in a magnetic field is investigated using both an analytic steepest-descent method and computer simulation techniques. The free energy is derived analytically by means of a mapping onto the soliton-bearing double-anisotropic ferromagnet. The specific heat is calculated numerically and the results are compared with the analytical findings and with experimental measurements on the linear-chain antiferromagnet TMMC in order to evaluate the validity of the analytical theory and to assess the importance of quantum fluctuations in TMMC.