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 Gorkovs 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.
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