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Another option would be to manually remove one of the rows if you have a client viewer (e.g., Server Management Studio for MS SQL).
In MS SQL you could use a CURSOR to go through and delete one of the rows. Not sure is MySQL has anything similar (sort of like a looping routine).
A brute force method is to delete both rows and re-insert the data.
ALTER TABLE `table` ADD UNIQUE INDEX `unique_index` (`column_one`, `column_two`, `column_three`);
For MySQL, you can even let the creation of this index delete the duplicates, just make sure you backup your data first in case you don't have the correct columns in the index!
ALTER IGNORE TABLE `table` ADD UNIQUE INDEX `unique_index` (`column_one`, `column_two`, `column_three`);