There have been very few reports (especially recently) of people being refused this, so the chances are that you will be OK. The fact that you're flying in F for LHR-ORD means that timing is not even arguably a problem. The only question is whether someone might refuse to check the bag for sector 2 only before sector 1 has been flown.
But make sure you have a contingency plan (eg using the Left Luggage on the arrivals level near the exit for domestic arrivals) in case you are refused. Hopefully, your original trip planning included a time allowance for this contingency plan.