This happened to me when I imported the file. Suddenly, I had two subdirectories containing copies of all my files. The compiler complained about repeating classes.
I found a solution, but it is a ball and a shell.
1: click on your project in the navigator to open the project settings in the main window.
2: Open the source compilation accordion record. (This allows you to see which files are used in the compilation process.)
3: Find all duplicates here and delete them. (At this point, your project should compile again.)
4: In your navigator, slowly, double-click one of the files that are duplicated there. This should allow you to rename it. Change the name slightly (not the extension).
5: You should notice that the copy turns red. Select it and click "Delete." (This avoids the delete operation by deleting the file from Compilation Sources)
6: Rename the source file back to the original name again.
7: Repeat from 4 until you're done, or until you get bored.
8: Explain to your boss why a simple copy change took half a day.
This process can be optimized by first renaming all duplicate files, and then deleting duplicates immediately. However, this means that you cannot verify successful compilation between steps, which allows you to narrow down the culprit to one file. And it takes even more time.
If compilation failed, make sure that all the necessary files are still in the "Compile Sources" section, as this process may lead to their loss. The compiler usually gives some reasonable errors regarding missing classes and variables, but missing AppDelegate will lead to a more confusing error.