Without reading the rules - a run is unearned only in an instance where an error directly or indirectly causes a run to score. when an error on a play causes a run to score on that play, or when the runner who reached on an error, or was put into scoring position via an error scores. Or when there are two outs and an error has occured in an inning, any runs scored in that inning after that are unearned. In this instance you could potentially have unlimited numbers of unearned runs. This being said, the only time you can have an unearned run score on a fielder's choice is when the runner on third reached on an error, or if an error is commited attempting the fielder's choice. You can also have fielder's choices with no outs being made if the runner beats the throw, but I think those are hits.
A Fleshner Fantasy wrote:yeah, it is. It is also an RBI, however a double play is earned, yet it is not an RBI.
eh? That's like Yogi Berra speak.
Haha, sorry that was badly written.
The answer to the original question is yes. In addition, for a fielder's choice, the batter is awarded an RBI. However, on a double play, it is still an earned run, however no RBI is granted. Make sense?