Unless it's something like the Josh Rosen situation with the Cardinals, I'm usually not in favor of teams trading a quarterback that they took in the first round after one season. I think that the Chicago Bears should trade Justin Fields before the draft both for his sake and for the sake of the team.
It would be best for Fields because the Bears are likely to destroy his career. The Bears were bad last season. Fields was once sacked nine times in one game. He had Allen Robinson to throw to and now he's gone. The Bears have only gotten worse. There are quarterbacks who can make lemonade when you give them lemons; but, even Aaron Rodgers needs help. The Bears also don't have a first round pick this year because of the trade for Fields last season; so, they don't have many ways to get him help on the line or at receiver. Basically, Fields is being dealt a terrible hand for a young player.
The Bears would benefit for several reasons. They probably could get a first round pick for Fields. Fields is still on a cheap, rookie contract and this is a weak draft class at quarterback. Any team thinking about burning a first round pick on a quarterback should entertain the possibility of just trading that pick for Fields.
The Bears are already clearly pushing the reset button. Mack is gone. Robinson is gone. They're trading talent for what they can get. Their new head coach is a defensive mind. They know they're building something different and that they're going to suck this year. If anything, they might as well suck badly enough to get a better draft pick next season.
Finally, although it's rare that a player refuses to play for the team that drafts him, it does happen. If the Bears ruin Justin Fields' career having never given him a chance to develop, I can see a quarterback selection in the near future who would refuse to play for them. Free agents aren't going to want to go there if they signal to the world that they'd rather destroy your career than admit to making mistakes.
Just do the right thing, get on the phone, and start shopping Fields around to one of the many teams that would love to have him.