Palumbo will start for Texas in their series opener against the Seattle Mariners on Monday and Adrian Sampson will get at least a spot start on Tuesday.
Chavez gave up six earned runs in 5 1/3 innings against the Houston Astros on July 12 and didn't make it out of the first inning against the Arizona Diamondbacks on Wednesday (7 ER in 2/3 of an inning).
In his most recent appearance with Triple-A Nashville on Sunday, Palumbo gave up one earned run in four innings pitched and struck out six. In his previous start on July 1, Palumbo didn't allow a run in five innings of work while striking out 10.
Palumbo last appeared with the Rangers in a game against the Minnesota Twins on July 7. He threw three innings out of the bullpen, allowing just one hit and struck out two.