  With the linear sigma model, we have studied Bose-Einstein condensation and
the chiral phase transition in the chiral limit for an interacting pion system.
A $\mu-T$ phase diagram including these two phenomena is presented. It is found
that the phase plane has been divided into three areas: the Bose-Einstein
condensation area, the chiral symmetry broken phase area and the chiral
symmetry restored phase area. Bose-Einstein condensation can happen either from
the chiral symmetry broken phase or from the restored phase. We show that the
onset of the chiral phase transition is restricted in the area where there is
no Bose-Einstein condensation.
