You are correct. Someone who’s "bet the chalk" has wagered on the favorite in a contest. In your example, the talk-show guy was saying that he was picking all the favorites for the weekend’s games.
The term also means having a proclivity to bet favorites, and given that it’s the typical betting style of the public, it’s also sometimes used derogatorily. For example, a professional might imply that someone bets like a tourist by referring to him with a term like Chalk Boy, Mr. Chalk, or the most colorful one we’ve heard, Chalkbob Squarepants ("square" being another reference to an unskilled sports gambler).
As to where the term originated, there are two beliefs, both going back to the days before electronic betting boards, when chalkboards were often used to post odds.
The first is that it came from horse-race betting, where, as odds changed, the new favorite would be rewritten in chalk. We’ve heard that one a lot, so we’re sure it’s valid.
We like the second possible origin better. When sports books posted lines on chalkboards, they always wrote the spreads next to the favorites. So rather than write something like Packers -3 and Bears +3, they’d only put -3 next to the Packers, or simply write "Packers 3." So the favorite was indicated by the (extra) chalk.
The sports book explanation has value in reading lines even today, as you can often easily determine who’s the favorite in a game by glancing at the board and seeing where the pointspread number is positioned.
