Fantasy leagues have a complicated structure in which "owners" constantly tinker with their active lineups to garner the most points from each week's games. Much time is spent in purchasing and activating players for the next week's games. Here is the definition of chalk given at Daily Fantasy Sports 101's "Daily Fantasy Sports Glossary: Making Sense Of The Language Of The Game" page:
Chalk – Refers to the favorites or the picks that everyone has on their line-up. If a player is ‘chalky’ that means he has a high ownership percentage
So chalkiest refers to the most widely owned and activated player (at a particular position) during a particular week.
The term chalky may well have come from sports gambling. Google search results indicate that a "chalk play" is a sports gambling bet on a favorite to win or cover the point spread—it's the opposite of a "dog [or underdog] play." The bigger the favorite you're betting on, the "heavier the chalk"—or the "chalkier" the bet is.
Many gamblers like to bet on longshots or underdogs because the payoff on the bet is so much higher. In a baseball game, for example, a bad team starting an indifferent pitcher against a good team starting an excellent pitcher might have odds of +230 for the dog and –240 for the chalk: That means that you can bet $100 on the bad team to win $230 if it does win; conversely, you can bet $240 on the good team to win $100 if it does win. The good team is very likely to win under the circumstances, but the payoff isn't great for the money put on the line.
I found a sports betting thread that uses "chalk" and "heavy chalk" in the sense of heavy favorite in response to the question "Do you know 'many' or 'any' successful pro bettors that bet nothing but BIG FAVORITES?"