Try, "It wasn't long before Chiyo became the most popular geisha in Kyoto."

Hi Denise, It slightly depends on what tense you want to use. Using the present tense we could write something like this: "After only a short time passes, Chiyo becomes the most popular geisha in Kyoto." "After only a short time, Chiyo becomes the most popular geisha in Kyoto." (Past tense) "Not much time passed before Chiyo became the most popular geisha in Kyoto." (Past perfect) "Not much time had passed when Chiyo became the most popular geisha in Kyoto." (I wouldn't recommend this tense as it suggests that she became popular overnight [in a very short space of time]) The present or past tense works well here if you're telling a story. I hope this makes sense.

The other comments are good and helpful. I just want to suggest that you post several more lines of your text so we can see the context. It might help :)