A method for producing an Fe-based nanocrystalline alloy ribbon, the method comprising: supplying a molten Fe-based alloy onto a rotating chill roll, and rapidly solidifying the molten Fe-based alloy that has been supplied onto the chill roll, thereby obtaining an Fe-based amorphous alloy ribbon having a free solidified surface and a roll contact surface, and having a width of from 5 mm to 65 mm and a thickness of from 10 μm to 15 μm; and heat-treating the Fe-based amorphous alloy ribbon, thereby obtaining an Fe-based nanocrystalline alloy ribbon; wherein an outer peripheral part of the chill roll comprises a Cu alloy, and a thermal conductivity of the outer peripheral part is in a range of from 110 W/(m·K) to 225 W/(m·K), a Vickers hardness of the outer peripheral part is in a range of from 250 HV to 400 HV, wherein the Vickers hardness is a value measured with a test load of 20 kgf, in the Fe-based nanocrystalline alloy ribbon, a number of protrusions P in the free solidified surface, each having a depression at a central part thereof, is 1.2 or less per 100 mm 2 of area, and warpage in a width direction is 0.30 mm or less per 10 mm of width, wherein the number of protrusions P in the free solidified surface and the warpage in the width direction are obtained as specified in description, and the molten Fe-based alloy has an alloy composition represented by the following Composition Formula (A): Composition Formula (A): Fe 100-a-b-c-d-e Cu a Si b B c Nb d C e wherein, in Composition Formula (A), each of 100-a-b-c-d-e, a, b, c, d, and e represents an atomic percent of a relevant element when a total of Fe, Cu, Si, B, Nb, and C is 100 atom%, and a, b, c, d, and e satisfy 0.30 ≤ a ≤ 2.00, 13.00 ≤ b ≤ 16.00, 6.00 ≤ c ≤ 11.00, 2.00 ≤ d ≤ 4.00, and 0.04 ≤ e ≤ 0.40, respectively. supplying a molten Fe-based alloy onto a rotating chill roll, and rapidly solidifying the molten Fe-based alloy that has been supplied onto the chill roll, thereby obtaining an Fe-based amorphous alloy ribbon having a free solidified surface and a roll contact surface, and having a width of from 5 mm to 65 mm and a thickness of from 10 μm to 15 μm; and heat-treating the Fe-based amorphous alloy ribbon, thereby obtaining an Fe-based nanocrystalline alloy ribbon; wherein an outer peripheral part of the chill roll comprises a Cu alloy, and a thermal conductivity of the outer peripheral part is in a range of from 110 W/(m·K) to 225 W/(m·K), a Vickers hardness of the outer peripheral part is in a range of from 250 HV to 400 HV, wherein the Vickers hardness is a value measured with a test load of 20 kgf, in the Fe-based nanocrystalline alloy ribbon, a number of protrusions P in the free solidified surface, each having a depression at a central part thereof, is 1.2 or less per 100 mm 2 of area, and warpage in a width direction is 0.30 mm or less per 10 mm of width, wherein the number of protrusions P in the free solidified surface and the warpage in the width direction are obtained as specified in description, and the molten Fe-based alloy has an alloy composition represented by the following Composition Formula (A): Composition Formula (A): Fe 100-a-b-c-d-e Cu a Si b B c Nb d C e wherein, in Composition Formula (A), each of 100-a-b-c-d-e, a, b, c, d, and e represents an atomic percent of a relevant element when a total of Fe, Cu, Si, B, Nb, and C is 100 atom%, and a, b, c, d, and e satisfy 0.30 ≤ a ≤ 2.00, 13.00 ≤ b ≤ 16.00, 6.00 ≤ c ≤ 11.00, 2.00 ≤ d ≤ 4.00, and 0.04 ≤ e ≤ 0.40, respectively. <EOS>