As planning for the Pioneer 10 and 11 missions progressed, mission scientists found themselves desiring a third probe. In 1971, a formal mission study was proposed for a spacecraft to be launched to Jupiter in 1974, where it would use the gas giant as a gravitational slingshot to travel outside the ecliptic. This was the first Out-Of-The-Ecliptic mission (OOE) proposed, for Jupiter and solar (Sun) observations.
NASA/Ames Research Center would have managed the project. The NASA contractor TRW Systems Group (formerly Space Technology Laboratories) would have constructed Pioneer H from the flight-qualified spare components intended for the Pioneer F and G probes (designated Pioneer 10 and Pioneer 11 after launch).
Pioneer H at NASM, behind James A. Van Allen
NASA management did not approve the mission proposal, and it was never launched in 1974. In 1976 NASA transferred the craft (without RTG) to the Smithsonian Institution. In January 1977, Pioneer H was moved to the National Air and Space Museum, where it was eventually displayed as a replica of Pioneer 10.
The Pioneer H mission concept was finally realized with the Ulysses mission, which achieved the OOE orbit originally envisioned for Pioneer H. And the Juno mission, currently on its way to Jupiter, will go into a polar orbit and from there undertake the magnetometer observations that Pioneer H would have performed.
While described in official Smithsonian records as a "replica", the spacecraft was considered fully functional by Pioneer mission planners (though its RTGs were never installed). Mark Wolverton quotes James Van Allen in The Depths of Space: 
"We mounted an intensive campaign to launch the flight-worthy spare spacecraft and its instrument complement on a low-cost, out-of-ecliptic mission via a high-inclination flyby of Jupiter. However, our case fell on deaf ears at NASA headquarters, and the spare spacecraft now hangs in the main gallery of the National Air and Space Museum, at 1 AU and zero ecliptic latitude."