  Superconductivity in the t-J model is studied by extending the recently
introduced extremely correlated fermi liquid theory. Exact equations for the
Greens functions are obtained by generalizing Gor'kov's equations to include
extremely strong local repulsion between electrons of opposite spin. These
equation are expanded in a parameter $\lambda$ representing the fraction of
double occupancy, and the lowest order equations are further simplified near
$T_c$, resulting in an approximate integral equation for the superconducting
gap. The condition for $T_c$ is studied using a model spectral function
embodying a reduced quasiparticle weight $Z$ near half-filling, yielding an
approximate analytical formula for $T_c$.
  This formula is evaluated using parameters representative of single layer
High-$T_c$ systems. In a narrow range of electron densities that is necessarily
separated from the Mott-Hubbard insulator at half filling, we find
superconductivity with a typical $T_c$$\sim$$10^2$K.
