  The Bethe-Salpeter equation restores exact elastic unitarity in the $s-$
channel by summing up an infinite set of chiral loops. We use this equation to
show how a chiral expansion can be undertaken in the two particle irreducible
amplitude and the propagators accomplishing exact elastic unitarity at any
step. Renormalizability of the amplitudes can be achieved by allowing for an
infinite set of counter-terms as it is the case in ordinary Chiral Perturbation
Theory. Crossing constraints can be imposed on the parameters to a given order.
Within this framework, we calculate the leading and next-to-leading
contributions to the elastic $\pi \pi$ scattering amplitudes, for all isospin
channels, and to the vector and scalar pion form factors in several
renormalization schemes. A satisfactory description of amplitudes and form
factors is obtained. In this latter case, Watson's theorem is automatically
satisfied. From such studies we obtain a quite accurate determination of some
of the ChPT $SU(2)-$low energy parameters (${\bar l}_1 - {\bar l}_2 =
-6.1\er{0.1}{0.3} $ and ${\bar l}_6= 19.14 \pm 0.19$). We also compare the two
loop piece of our amplitudes to recent two--loop calculations.
