Chekhov is considered to be the grandfather of the modern short story.  

As he is out of copyright, dozens of websites publish hundreds of his stories.  The Literature Network is probably the best I found (links to short stories are down the left side bar).

With such a prolific writer, it can be hard to know which story to start with.  I’d like to suggest Misery, a short, concise and, as the title suggests, miserable piece.  If you like that, maybe try (in no particular order): The KissThe Lady with the DogGooseberriesThe Man in a CaseWard No.6The Duel and The Steppe.