The 520-hour private pilot lost directional control of the single-engine tailwheel equipped experimental airplane during the landing roll on. The pilot reported that while in the pattern for the 3,999-foot long, by 50-foot wide runway, the tailwheel developed an excessive shimmy resulting in the loss of directional control. The pilot added that during his fifth touch and go, he first noted that the airplane started a slight drift to the left, which was followed by an uncommanded turn to the right. The airplane exited off the right side of the asphalt runway, into the grass. The airplane subsequently nosed-over and came to rest in an inverted position. The pilot and passenger were able to exit the airplane unassisted. An examination of the airplane revealed that the engine firewall sustained structural damage during the accident sequence. Additionally, the right steering chain was found separated from the steering arm of the tailwheel assembly. The reason for the separation could not be determined. The winds at the time of the accident were reported as light and variable.