This film, which is also being shown on April 21st and 25th, is part of the Krzysztof Kieslowski season at Close-Up Cinema. You can find all the details of the season here.
Chicago Reader review:
An exquisite enigma by Krzysztof Kieslowski (Decalogue) following the parallel lives of two 20-year-old women, one in Poland and one in France, both played by the beautiful Irene Jacob. The Polish Veronika is a talented singer with a heart condition; the French Veronique quits her voice lessons and gets involved with a puppeteer who writes children's books. Masterfully directed, this rather dreamlike 1991 French-Polish production explores a dual nature that seems to grow uncannily out of the coproduction situation itselfâ€”almost as if Kieslowski were dreaming of a resurrected artistic identity for himself as Polish state financing went the route of Polish communism. With Philippe Volter, Halina Gryglaszewska, Kalina Jedrusik, and Aleksander Bardini.
Here (and above) is the trailer.