A P odd anapole moment of the deuteron is found in the chiral limit, m_π → 0. The contact current generated by the P odd pion exchange does not contribute to the deuteron anapole. Being combined with usual radiative corrections to the weak electron-deuteron interaction, our calculation results in a sufficiently accurate theoretical prediction for the corresponding effective constant C_2d. The experimental measurement of this constant would give valuable information on the P odd πNN constant and on the s-quark content of nucleons. We calculate also in the same limit m_π → 0 the deuteron P odd and T odd multipoles: electric dipole moment and magnetic quadrupole moment.