We have a roundtrip ticket from Chicago to Rome but will be in Venice on the last 3 nights of our trip. With that in mind, I saw a flight leaving Venice at 6:20 AM arriving in Rome (FCO) at 7:25 AM. Our flight to Chicago leaves at 9:45 AM out of FCO also. I noticed ITA Airways is out of Terminal 1 and United Airlines is out of Terminal 3. Will this be enough time for us to go through customs and everything else we may need to do for our United flight back home to Chicago?

you don't go through customs - that's for checking goods you import into a country.

you will need to wait for baggage claim, check in with UA, check your bags, and go through emigration, and security however. There might be a secondary passport check and security for US bound flights - there used to at many airports but I don't know if that's still the case.

If you have no checked bags, and can check-in online with UA ahead of time, and your Venice to Rome flight is on time, then as long as you are at the gate by the time they close it , which might be 15 min or more before scheduled departure, then yes, you have plenty of time. But that's a lot of ifs. If you have checked bags you need to collect in Rome, forget it.

The real question is not whether you have enough time, but what will you do if you don't.... Say if your Venice to Rome flight is delayed, and you miss your UA flight back to Chicago? UA might call you a no show and you'd need to buy another ticket.

Why not change your UA flight to depart from Venice. It may mean connecting through somewhere like Munich on their partner airline Lufthansa.

This is not a good plan. Unless you can change your flight home to go from Venice, you need to be in Rome the night before your flight. Otherwise, as noted, if your flight out of Venice is delayed and you miss your flight out of Rome, since they're not on the same ticket, you will have to buy a new, probably very expensive, ticket to get home.

The question is not whether there is enough time between arrival and departure. The question is whether you want to risk missing the United flight. If you miss the connection, United won't care, and you might have to spend a lot more to re-book on a later United flight FCO-ORD. To be protected in the event of a delay, you'd have to book this as a single, multi-city ticket.

Since United doesn't fly Venice to Rome, you could head to Venice immediately on landing at FCO at the start of the trip and put your Rome nights at the end. Or head to Rome the night before your FCO-ORD flight. You could also explore J62's suggestion of changing your United ticket and flying home from Venice via Frankfurt or Munich on United's partner Lufthansa. We did this on one trip, but it still involved a crazy-early departure from Venice... not the way I like to end a trip.

Others are already giving you 100% great and correct advice and information. Even if this risky plan went like clockwork, why end your trip with such stress?

So, what options do you have?
It is best to revise your itinerary a bit (even if you have to change hotel days). Since you have RT into/out of Rome, on arrival in Rome, go directly on to Venice and work your way back to Rome, reserving all time in Rome for the end of the trip. You could also go directly on to Florence, then Venice and back to Rome, still Rome at the end.

If it is absolutely impossible to rearrange things, I hate advising cutting any time from Venice, but your last night will be kind of shot anyway and so stressful, I would cancel your last night in Venice and catch a fast, direct train, departing Venice late afternoon (5:00 or 6:00 pm), in time to check into a hotel and have dinner in Rome. You will get a better night’s sleep (probably better food too) with a lot less stress.

For the future, when you have an early flight, especially an international flight, it is almost always better to be in your departure city the night before, and put all time in that city at the end.
If you can make multi-city (not multiple one-way) tickets work, and not backtrack, that saves time and money sometimes.
OTOH, you work with what you have. Hope your trip is wonderful!

The rule of thumb is three hours before US flights.

The only way you should consider your plan is if ITA and United had a partnership agreement and I don't think they do.

Not to pile on, but NO this is NOT a reasonable plan. Even if your ITA flight landed on time, you'd still have a hard time getting checked in for your UA flight on time. UA flies out of Venice, either see about changing your itinerary to that (you'd have to connect in EWR) or plan to get to Rome the evening before your UA flight. You could grab a train, Venice to Rome nonstop leaving around 5 pm and arriving Rome around 9 pm. Plenty of hotels around FCO.