The Back Story (Short Version): This was recorded, in 1966, for a quickie album cashing in on the Batman TV show, and it was billed to The Sensational Guitars of Dan and Dale. In reality, it was performed by members of a well known avant-garde jazz band and a well known sort of underground rock band of the period. You may not be able to guess who the musicians are immediately, but at about the halfway point of the track, when the solo guitar comes in, you should recognize at least one of the players.
Hint: It was produced by Tom Wilson.
[h/t Willard's Wormholes]