No more non-stop between Chicago and Rome?

Might be too early to book that flight.

When are you looking in 2020? More than a year?

It's possible the nonstop is seasonal. American's nonstop is seasonal.

I didn't think that any airline schedule was firm until 11 months out or 330 days. You may be too early if looking for the summer of 2020.

We're traveling in mid-April. I'm within 11 months of flight dates, which is almost always when I book my flights . . .when booking first opens up. I've flown non-stop from Chicago to Rome a few times, but yes, those were high tourist season trips, summer and early fall. I'll hold off booking a flight with a layover in hopes of seeing a non-stop option in the future.

Might have something to do with Alitalia's problems. They used to fly year round, but now are not showing past Sept 29. United and American are seasonal, ending in late October.
American starts back up again March 29, but after April 4, prices skyrocket until April 27. when United seasonal service begins.
It might be a quirk in American's reservation system. Flights on Matrix-ITA from April 5 do not show American Airlines, but do show very high prices by Finnair. Click on the flight details of the Finnair flights and they show operated by American Airlines. That is odd, to say the least.

I've learned over time to not book too far in advance. 'As soon as possible' may not show all options, or you book a line that is at risk, or the airline changes schedules. This happens to me more often than not and sometimes they are drastic flight changes. But perhaps it is worse as my city rarely has direct flights on long hauls. So I can't understand the aversion of a non-stop.
I also make Matrix ITA my first research stop. You can use 'non-stop' as a filter.
What about some other option like Milan or Venice direct and train to Rome?

I too don't think there is any upside from booking very far out (or narrowly by a single airline unless you're using points or there's a really good reason). No money savings since they don't need to discount fares way in advance (before demand can be predicted) and risk in schedules changing. Plus you're plunking down all that money upfront. I would just wait and see how it shakes out.

American's seasonal route to FCO generally beings in mid-May and ends in mid-October. I believe Alitaia, Delta's Italian code-share partner, made its direct flight to Rome seasonal a couple years ago at the onset of their financial troubles. However, I might be a little hesitant to purchase tickets on Alitalia given their current situation...

As to where to change if one is required, I prefer a change in Europe to a change in US. There are typically multiple flights per day between major cities in Europe but often only one flight per day between one's US and European airports. I think it's much easier to make a change at AMS versus CDG. I've observed that some airlines aren't booking passengers who miss US connections on other airlines' international flights, so a missed US connection could result in a couple of days delay in reaching Europe.

Never thought of that, Frank, excellent point. I will say, if given a choice, I connect in a city other than Paris. It's not that I dislike the Paris airports, its more that there is a higher risk of striking workers.