Air carrier Captain reported safely returning to departure airport after experiencing a very pronounced aircraft vibration from the left engine on takeoff. Post-flight inspection revealed fan blade damage from a suspected bird strike.

Narrative

On takeoff at ZZZZ; at rotation or immediately thereafter; I noticed a very pronounced aircraft vibration. This vibration was felt and also heard. The left engine vibration indication was indicating 5.0 with climb power set. I later learned the vibration and noise were much more pronounced in the back of the aircraft; especially near the overwing seats. Staying aware of terrain; we continued climb with a lesser power setting; and were able to reduce the vibration. Basic trouble-shooting revealed the vibration would increase and decrease with the power setting; but was always present. Consultation with Dispatch and Maintenance Control was accomplished. It was decided that some sort of engine event was occurring; and that a return to ZZZZ was warranted. Priority handling was requested as a precaution. We dumped approximately 44K of center tank fuel in a holding pattern at ZZZZZ. We landed overweight (335K) uneventfully; and taxied back to the gate. Upon block in; Maintenance reported damage to the left engine fan -- suspected bird strike.