"Chuck E.’s in Love" is a song by Ricky Lee Jones.
After careful analysis of the lyrics, I have concluded that this is a love song about the American architect and designer, Charles Eames (1907-78), as told by his wife, Ray.
As evidence, I present you with the following:
First, in 1941, Mr. Eames won the Museum of Modern Art’s Organic Design Competition for his molded plywood chairs. These chairs were not manufactured due to the difficulty in shaping plywood, but this is precisely what inspires Ray (I speculate) to begin the song: "How come he don’t come and p.i.p. with me down at the meter no more?" Here, p.i.p. clearly stands for "produce in plywood."
Next, we know that Mr. Eames was active in set design for the motion picture industry in the '40s and '50s. This explains the second line, "How come he turn off the t.v.?" - with the answer being, because he saw television as a threat to his livelihood.
Finally, he contributed to IBM’s New York World’s Fair exhibit in the '60s and their American Bicentennial Exhibition in the '70s. He was quite proud of this, which is what Ms. Jones is referring to with the line, "He sure is acquired a cool and inspired sorta jazz when he walk."
I’m afraid that I am running short on space — otherwise I would continue providing you with even more convincing evidence. But if you are still interested, I suggest that you get a copy of the song, listen carefully, and see for yourself.
(And if you don’t accept that, I’m also working on a hypothesis that Chuck E. is really Charles Estaing, commander of the French fleet, who helped the colonies during the Revolutionary War.)