The name Chevy Chase actually comes from an ancient Scottish ballad called "The Ballad of Chevy Chase". The "chase" refers to a hunting party, and the "Chevy" is from the Cheviot Hills, which are located along the English/Scottish border. More context:
The chase is led by Percy, the English Earl of Northumberland. The Scottish Earl of Douglas had forbidden this hunt, and interprets it as an invasion of Scotland. In response he attacks, causing a bloody battle which only 110 people survived.More from The Straight Dope:
They are thought to have been based on the events of the Battle of Otterburn in 1388, although the account of the battle is not historically accurate and it may relate to border skirmishes up to fifty years later.
Whatever its factual basis, the story of Chevy Chase became a cherished part of Scottish folklore, and people of Scottish ancestry applied the name to various places in America. The best known example is Chevy Chase, Maryland, a planned community established as a green refuge from Washington DC. It's one of the priciest residential areas on the east coast (location, location, location) and still fairly green and park-like.Many early Glendale residents were of Scottish ancestry, including L.C. Brand.
Interestingly, the word glendale appears in the text of the ballad!
Wher syx and thrittè Skottishe knyghtesFrom a later version:
on a day wear beaten down;
Glendale glytteryde on ther armor bryght,
over castille, towar, and town.
Of fifteen hundred EnglishmenSo there you have it: Chevy Chase Drive is named after a tale of Scottish knights kicking ass, not the star of Fletch.
Went home but fifty-three;
The rest were slain in Chevy Chase
Under the greenwood tree.
*Update: Poking through my copy of A Brief History Of Adams Square, I've learned that some parts of Chevy Chase Drive were originally named Park Avenue and Sycamore Canyon, but in the mid 1920's a real estate agent named E.R. Austin worked to create an additional entrance into Glendale from Los Angeles and was able to convince L.A. and Glendale officials to change the name of this route to Chevy Chase Drive for the entire length of the street, as well as extend the street in various places. All this combining of names and extending made Chevy Chase Drive the longest street in Glendale.