We present local existence and uniqueness results for solution of Stochastic Navier-Stokes Equations with additive random noise in some Besov spaces. The work is carried out through a blending of Harmonic Analysis tools such as Littlewood Paley Theory, Jean-Michel Bony Paradifferential Calculus and Stochastic Calculus. A key role is played by the Stochastic Heat Equation in probabilistic evolution spaces of Besov type.