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Explanation: As Chester is a place name, "Chester's Diary" doesn't fit. "My Diary from Chester" doesn't really sound quite right unless the author is talking about sending the diary to somewhere from Chester.
"My Chester Diary" (with the meaning of My Diary about Chester, for example impressions about the town and its people written down by the author) is what you're looking for here.
Explanation: This is German, so there's no doubt someone might move this to the German->English Forum. "Chester's Diary" is the best of the 3 options presented w.r.t. English grammar, but in German this says "Diary about Chester". So I would rule all of them out and say,
"My Diary about Chester"
Bryan Crumpler United States Local time: 08:44 Native speaker of: English