A chain tensioner comprising: a tubular cylinder having a bottom; a tubular plunger axially slidably inserted in the cylinder, the tubular plunger having an open end inserted in the cylinder, and a closed end protruding beyond the cylinder; an internal thread on an inner periphery of the plunger; a screw rod including, on an outer periphery of the screw rod, an external thread threadedly engaged with the internal thread; and a return spring disposed between the screw rod and the plunger, and configured to bias the plunger in a direction in which the plunger protrudes from the cylinder, wherein the internal thread comprises: a push-in-side flank configured to receive pressure when a load that tends to push the plunger into the cylinder is applied; a protruding-side flank configured to receive pressure when a load that tends to cause the plunger to protrude from the cylinder is applied; and a thread top face between the push-in-side flank and the protruding-side flank, and wherein the push-in-side flank has a flank angle (θ1) larger than a flank angle (θ2) of the protruding-side flank, characterized in that each of the push-in-side flank and the protruding-side flank of the internal thread comprises a rolled surface having a surface roughness smaller than Ra1.0 μm, wherein the internal thread further includes, at a position of the internal thread at which the protruding-side flank intersects with the thread top face, a chamfer configured to receive a bulge from the protruding-side flank during rolling. a tubular cylinder having a bottom; a tubular plunger axially slidably inserted in the cylinder, the tubular plunger having an open end inserted in the cylinder, and a closed end protruding beyond the cylinder; an internal thread on an inner periphery of the plunger; a screw rod including, on an outer periphery of the screw rod, an external thread threadedly engaged with the internal thread; and a return spring disposed between the screw rod and the plunger, and configured to bias the plunger in a direction in which the plunger protrudes from the cylinder, wherein the internal thread comprises: a push-in-side flank configured to receive pressure when a load that tends to push the plunger into the cylinder is applied; a protruding-side flank configured to receive pressure when a load that tends to cause the plunger to protrude from the cylinder is applied; and a thread top face between the push-in-side flank and the protruding-side flank, and wherein the push-in-side flank has a flank angle (θ1) larger than a flank angle (θ2) of the protruding-side flank, characterized in that each of the push-in-side flank and the protruding-side flank of the internal thread comprises a rolled surface having a surface roughness smaller than Ra1.0 μm, wherein the internal thread further includes, at a position of the internal thread at which the protruding-side flank intersects with the thread top face, a chamfer configured to receive a bulge from the protruding-side flank during rolling. a push-in-side flank configured to receive pressure when a load that tends to push the plunger into the cylinder is applied; a protruding-side flank configured to receive pressure when a load that tends to cause the plunger to protrude from the cylinder is applied; and a thread top face between the push-in-side flank and the protruding-side flank, and wherein the push-in-side flank has a flank angle (θ1) larger than a flank angle (θ2) of the protruding-side flank, characterized in that each of the push-in-side flank and the protruding-side flank of the internal thread comprises a rolled surface having a surface roughness smaller than Ra1.0 μm, wherein the internal thread further includes, at a position of the internal thread at which the protruding-side flank intersects with the thread top face, a chamfer configured to receive a bulge from the protruding-side flank during rolling.