Chiliasm is a really bad heresy. People who believe in this may believe that the Antichrist's reign is that 1000 year reign. Likewise, people who believe they will be raptured before the tribulations will not believe anyone is the Antichrist ever, because they expect to fly up into the air before that starts, so they are more likely to submit to the Antichrist.
The Church recognizes the 1000 year reign to be the current period we are in.
The heresy is based on Revelation 20:2-3
What it is actually describing is Christ defeating death by death by his resurrection and chaining Satan, to be let out for a little while in the last days.
The person I linked to repudiates Pre-Tribulation rapture. And I think he assumes that the Antichrist's Reign will come first.
If this is the 1000 year reign I expect people will be beating their swords into ploughshares under Christ's Reign. And ultra-long lives that still feature human death soon enough.
There is a lot of promises that haven't been fulfilled that I think even the Anti-Christ cannot fulfill. Which is why I am a Pre-Millennial in terms of the end times.