Kilian (shoulder) struck out two over two perfect innings in his rehab start Tuesday with High-A South Bend.
Kilian tossed 21 pitches in the outing while the Cubs continue to ease the right-hander along slowly as he makes his way back from a teres major strain in his right shoulder, an injury that has sidelined him since early March. The 27-year-old will likely require at least three more rehab starts to get fully stretched out for a traditional starter's workload, so he may not be activated until late July or early August. Once Kilian is reinstated, the Cubs could elect to option him to Triple-A Iowa, if the big club doesn't have an opening in its rotation.