ftl drive - Which race in Star Trek universe was the first to invent Warp technology?

Technically the first race to discover warp drive would be the ancient race in The Chase in Star Trek: The Next Generation. This is the species that moved out into the galaxy, explored it, and found it empty, so they seeded planets with DNA (which also explains why there are so many humanoid races in the galaxy).

But if you're talking races that are currently active on an interstellar scale, according to Memory Alpha, here's a simple table taken from the article on warp drive:

Vulcans: 9th century B.C.
Romulans: Didn't split from Vulcans until after Warp Drive.
Klingons: 9th century A.D.
Vissians: 12th century A.D.
Borg: 15th century A.D.
Humans: 21st century A.D.

(Note: Changes since original posting! The Memory Alpha article is confusing, one way it can be read is that Vulcans had an interstellar civilization in the 9th century B.C., but still didn't have warp drive until after A.D. 1947. It also took Vulcans a century to go from breaking lightspeed to reaching speeds as fast as warp 2.)

Data on other races and when they developed warp drive is apparently not available.