Played this several times my first time at it and could only get 2nd or 3rd, but I just played again today and got Gold on the 4th or 5th try with stock settings (manual, 0 TC, 1ABS, no aids). It's just a matter if slotting through different cars at the right time. The 3rd corner (slight bend before Chicago) is absolutely key.
What I do is I pass the first car at the first left hander after the right bend. Take the inside line, staying fairly straight to keep the car under control, brake, then slot in front of him from the inside, being gentle with the throttle. Then for the next slight left before Chicago you need to be very strategic. Remember that you can drive through the pylons where the line ends (not the inside ones through), however you need to be very smart here and this is why I said you need to be strategic.
If you just plow through the pylons for the inside line when you're close enough to the next car, there's no way through. You'll pass the first car, but the next two cars ahead will turn in and leave you with nowhere to go -- smash, DSQ. What you need to do is move through the pylons to get around the 10th place car, lift off the gas (while you're passing him), and turn right to get around around the next two cars moving into Chicago, then take the inside through the tires. Remember that slowing down is key here -- not too much but enough so that you can pass the 10th place car and then shift around the next two cars on the right side, keeping your momentum into Chicago to pass both of them on the inside.
You should be able to take the next car, which first runs wide, on this corner. Keep on the inside and don't worry if he comes in to nudge you (quite hard actually) since you won't fail (from my experience). From here on you're pretty much good to go. You've done most of the work, and I believe you should be 7th. You should be able to pass the next 2 cars under braking on the outside for Hammerhead. Stay on the right of them while braking, stopping a little later than they do, then slot in 5th for the corner entry on the inside of the next part of the corner.
Be gentle with the throttle here to keep the car in check. You don't need to worry about passing the next car very soon, so relax. You should start to get closer to him towards the exit of the followthrough, and then once you fly through the tires you should really gain on him, especially as he starts to brake for Bacharach, where you should take him under braking for 4th (inside or outside really -- outside can be nice since you keep your momentum and have a good cornering angle for the next corner). The 3rd place car might be struggling a bit on the exit and you should be able to nab 3rd place on the inside of Gambon, leaving you only 2 more cars to pass on the 2nd lap.
Here it all depends on how comfortable you feel. I believe I passed the 2nd place car on the first/second corner (much like the first lap and the 11th place car) or the slight bend before Chicago (through the pylons if you need to), and then the 1st place car during Chicago, coming out of the corner in the lead. If not there, you should be able to grab the lead under braking at Hammerhead (from the outside moving to the inside for the second part of the corner), and if not there you still have Bacharach again and then Gambom which are both great passing places.
THIS CHALLENGE CAN BURN IN HELL!!! 
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