There is no evidence that Anton Chekhov ever met Sigmund Freud. Although they were born around the same time, their lives were separated by country and by politics, so the likelihood of their meeting is slim; I could not find any evidence or report of their meeting in my research.
Anton Chekhov lived most of his life in Russia, with periods in France and visits to various parts of Europe, but he is not recorded as having visited Austria, where Freud lived and worked. In addition, Chekhov was a doctor of the body, not of the mind, and so he would not have been likely to seek out Freud, at the time still developing the theories of psychoanalysis. Chekhov died in 1904, 35 years before Freud's own death.
Sigmund Freud was born in Příbor, a town in Moravia which is now part of the Czech Republic. He lived and worked in Vienna for most of his life, and although he was likely aware of Chekhov as a literary figure, I could not find evidence that he ever sought a meeting. Freud's life was marked by struggles with the academic community and finally the rise of Nazi Germany, which occupied Austria. When Chekhov died in 1904, Freud was still working on his theories and running a discussion group for psychiatrists.
Both figures had many famous meetings, such as Chekhov's meetings with Leo Tolstoy and Maxim Gorky, and Freud's meetings with Salvador Dali and Virginia Woolf. However, if the two ever met each other, I could not find evidence of it.