  We prove the local well-posedness of the periodic stochastic Korteweg-de
Vries equation with the additive space-time white noise. In order to treat low
regularity of the white noise in space, we consider the Cauchy problem in the
Besov-type space \hat{b}^s_{p, \infty}(T) for s= -1/2+, p = 2+ such that sp <
-1. In establishing the local well-posedness, we use a variant of the Bourgain
space adapted to \hat{b}^s_{p, \infty}(T) and establish a nonlinear estimate on
the second iteration on the integral formulation. The deterministic part of the
nonlinear estimate also yields the local well-posedness of the deterministic
KdV in M(T), the space of finite Borel measures on T.
