As Frank says, a whole lot depends on your flight from Rome arriving on time or early. Since it is on the same airline (American, I assume), they should know you are coming, in case the connection is close.
I came back from Munich on USAir in 2007; I doubt that too much has changed since then.
My biggest complaint is that coming from Europe, you'll go through customs and immigration in Philly. Like most (all?) US airports, customs is not a secure area, so you will end up outside of security and have to go back through to get to your gate. That will take the most time. But I think that is true of IAD as well.
I assume you are flying from PHL to CHA. It looks like flights to Chattanooga leave from Concourse C, which is roughly across the hall from where you come out of customs & security.
In 2007 I also had only a carry-on, I had 1½ hours or a little less, as I remember, and I was leaving for Denver from B or C, and I made it with time to spare. Since 2007, I've made several domestic transfers at PHL without a problem.
PHL is a long airport. If you are going from A (international flights) to F, you might have a problem. Check the flight status to see what gates you are using.
Good luck.
BTW, security personnel in PHL were easily the most verbally abusive I have experienced anywhere in the world. Half the personnel seemed to have no other assignment then to yell at the passengers.