In this note we consider the parabolic Anderson model in one dimension with time-independent fractional noise Ẇ in space. We consider the case H<12 and get existence and uniqueness of solution. In order to find the quenched asymptotics for the solution we consider its Feynman–Kac representation and explore the asymptotics of the principal eigenvalue for a random operator of the form 12Δ+Ẇ.