  Let $f(z) = z^2 + c$ be a quadratic polynomial, with c in the Mandelbrot set.
Assume further that both fixed points of f are repelling, and that f is not
renormalizable. Then we prove that the Julia set J of f is holomorphically
removable in the sense that every homeomorphism of the complex plane to itself
that is conformal off of J is in fact conformal on the entire complex plane. As
a corollary, we deduce that the Mandelbrot Set is locally connected at such c.
