We derive in this paper Gaussian estimates for a general parabolic equation u t − a(x)u x x = r(x)u over R. Here a and r are only assumed to be bounded, measurable and essinf R a > 0. We first consider a canonical equation ν(x)∂ t p − ∂ x ν(x)a(x)∂ x p + W ∂ x p = 0, with W ∈ R, ν bounded and essinf R ν > 0, for which we derive Gaussian estimates for the fundamental solution: ∀t > 0, x, y ∈ R, 1 / Ct^{1/2} e^{−C|T (x)−T (y)−W t| 2 /t } ≤ P (t, x, y) ≤ C /t^{1/2} e^{−|T (x)−T (y)−W t| 2 /Ct }where T is a corrector satisfying appropriate properties. We then show that any solution u of the original equation could be divided by some generalized principal eigenfunction ϕ γ so that p := u/ϕ γ satisfies a canonical equation. As a byproduct of our proof, we derive Nash type estimates, that is, Holder continuity in x, for the solutions of the canonical equation.