Where did Chopin work?

Um, not too sure in what sense you mean this question. He was not employed by anyone and had no skill or trade other than the gift of music.

If you mean where did he carry out his work as a composer, then the answer is varied. Composition took place mostly wherever he was living at the time; Warsaw, Vienna and Paris to name a few, but notable places of composition include the monastery of Valdemosa, on the Balearic island of Palma di Mallorca, where he stayed for the benefit of his health, but the weather during his time there was so abysmal that it actually made his health worse and had to return to France, where he settled for several years at the home of his friend and patron, the authoress Georges Sand, aka madame Aurore Dudevant, in Nohant. It was here, in the relaxed, quiet and comfortable surrounds that his most prolific writing took place.