First off, just to be clear, the chemical potential being equal to zero is different from not having a chemical potential at all (e.g. a photon gas)?
Now: physically, what does having chemical potential $\mu=0$ mean for a gas?
A Bose-Einstein condensate exists below a critical temperature $T_c$, at which $\mu$ hits $0$. What's the connection between chemical potential and Bose-Einstein condensation?