You won't be able to avoid security at ORD. China Eastern flies from Terminal 5, and your domestic flight will arrive at T1/T2/T3. While T1/T2/T3 are connected post security, terminal 5 isn't (a few airlines sponsor buses for T3 to T5 transfers but the buses are solely for passengers of those airlines). So you will have to exit security, take a train over to Terminal 5 and go back through security there.