We show that laser filamentation can be initiated and propagate through strong extended turbulence well above the typical atmospheric values. We suggest that the effect of turbulence on filamentation is characterized by the product of the structure parameter for the refractive indexC2n and the length L of the turbulence region. Half of the filaments are transmitted for C2nL⩽4.4×10−10m1/3. Moreover, the surviving filaments keep their key spectral properties including correlations inside the white-light continuum.