A process for producing a low-attenuation optical fiber by producing a soot core preform by chemical deposition on a substrate; removing the substrate from the soot core preform, thereby forming a central hole along the soot preform; drying and consolidating the soot core preform in a consolidation furnace to form a glass core preform; heating the glass preform in the consolidation furnace above a glass melting temperature to produce a reduction of the diameter of the central hole; and stretching the glass core preform to completely close the central hole.