The QCD Lagrangian containing quarks and gluons has an approximate $SU(3)_\text{L} \times SU(3)_\text{R}$ which is spontaneously broken by a non-vanishing quark condensate $\langle \bar{q} q \rangle \neq 0$ down to $SU(3)_\text{V}$ and at the same time explicitly broken by quark masses. Former leads to eight Goldstones bosons, that acquire small masses due to the explicit symmetry breaking. Now, this Lagrangian is not really useful in the low energy regime, for instance below $\Lambda_\text{QCD}$, since there the hadrons describe the degrees of freedom. Thus at sufficiently low energies one only needs to take the Goldstone bosons $\pi, K, \eta$ into consideration in order to describe dynamics.
What I am not understanding from here on is: In order to construct the effective Lagrangian containing the Goldstone boson fields (and external fields) one wants $\mathcal{L}_\text{eff}$ to be invariant regarding the chiral group $SU(3)_\text{L} \times SU(3)_\text{R}$ instead of the vector subgroup $SU(3)_\text{V}$. This bothers me, since the Goldstone bosons only "exist" once the chiral symmetry group is broken down to $SU(3)_\text{V}$ which would mean that the chiral group is not a symmetry of the theory anymore. So, why isn't it enough to construct an effective Lagrangian that is invariant under $SU(3)_\text{V}$?