The sentence alone is grammatically correct. However, the sentence is written in a very specific way. There are only certain contexts in which this sentence would be correct. Basically, by itself it is correct. I cannot know if it is correct within a paragraph if you don't provide it.

You will have to provide us with more context, if you want a valid answer.

Don't know exactly if that is right or not but I can express the meaning of your sentence by this way. "The fact that she has written a letter gives her a good chance." OR "Writing a letter has given her a good chance". What do u think?