Engine dies when headlights are turned on.

[18Fiatsandcounting]

It sounds like you may be OK for now, but I agree that the problem could come back. I didn't see this mentioned, but was the engine at idle when you turned on the lights and it died, or higher engine speeds? The reason I ask is that I have seen some Fiats idle "OK" at only a couple hundred rpm, but since there's very little engine power at those speeds, even a very slight load on the engine was enough to stall it (such as from an alternator). The combination of a weak battery, very low (weak) idle, and then a heavy electrical load on the alternator, just didn't work.

So, and I admit that this is a long shot, but also check that your idle speed is where it should be (likely 800-900 rpm) and that the idle mixture screw is set for a smooth idle. I'm still thinking the problem is electrical as mentioned by the other responses, but I figured that I'd toss out the idle speed issue just because I have seen it happen.

-Bryan