That's the 3rd Infantry Regiment. Specifically the 1st and 4th Bn of that Regiment that are posted in the Military District of Washington DC as an honors unit. The Fife and Drums are part of 4th Bn. 2nd Bn 3rd Infantry is posted to Ft Lewis and the 2nd ID.
The regt was formed in 1784 as the First American Regiment. It is the Oldest Unit on active duty.