The Ekosian Chancellery was the headquarters of both the Ekosian government and the Ekos National Socialist Party in 2268. It was where John Gill was thought to broadcast his Führer speeches to the Ekosians. Captain Kirk and Spock began their search for Gill here.
While Chairman Eneg was seen twice in the building and Secretary Daras easily gained admittance for Kirk and Spock in disguise, the Chancellery was not necessarily used for Party functions. (TOS: "Patterns of Force")
The aspect of the building, though, indicates that 2260s Ekos would merit a slightly different industrial rating than would 1930s Germany, as its windows appear to be equipped with 1967-vintage air-conditoners.
The Ekosian Führer headquarters were the lightly-redecorated real-world offices of the old Paramount Pictures, the next-door neighbor of Desilu. Lucille Ball sold Desilu – and Star Trek – to Paramount's owner in mid-1967 but it was not until December, when this episode was in production, that the new unit Paramount Televison completely merged the two studios and tore down the wall between the two buildings.