Delhomme injured his right ankle in last week's loss at Tampa Bay and missed practice this week. He is inactive Sunday, making rookie Colt McCoy the No. 2 quarterback against the Chiefs.
The more mobile Wallace, who spent seven seasons with Seattle, is making his 15th career start. He went 5-9 as a starter for the Seahawks.
Delhomme threw two interceptions, including a game-swinging one at the end of the first half, in his debut with Cleveland last week. The Browns signed him as a free agent in March.
The most notable inactive player for the Chiefs is defensive end Tyson Jackson, who had six tackles in Monday night's upset of San Diego. Former Browns end Shaun Smith is starting for Kansas City.