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It wasn't likely that ESPN was going to pick up another Cardinals vs. Cubs game for their Sunday night showcase, and recently the network announced that they would be carrying Dodgers vs. Giants at San Francisco at 7 p.m. CT Sunday, July 27.
This means a daytime game for the Cubs and Cardinals on that date and the Cubs this morning sent out an email confirming that the Sunday, July 27 game will be at 1:20 p.m. CT and will be televised by WGN.
That's the last "TBD" scheduled time on the Cubs' home schedule this year. There is one more "TBD" date on the road schedule, one week after this game, August 3 in Los Angeles, listed as such on both the Dodgers and Cubs websites.
However, ESPN's schedule for August 3 already shows them carrying Red Sox vs. Yankees that night. (Gee, what a surprise.) Thus I would expect that soon, the Cubs and Dodgers will announce a daytime starting time for their contest, likely 1:10 PT, which is the Dodgers' typical starting time for Sunday afternoon games. I'd also expect this one to wind up on WGN.