These are the playwrights who have been awarded the Nobel Prize for Literature. (Some of them wrote in genres other than drama.)
1903 Bjørnstjerne Bjørnson Norway 1904 (shared) José Echegaray y Eizaguirre Spain 1911 Maurice Maeterlinck Belgium 1912 Gerhart Hauptmann Germany 1913 Rabindranath Tagore India 1915 Romain Rolland France 1921 Anatole France France 1922 Jacinto Benavente Spain 1923 William Butler Yeats Ireland 1925 George Bernard Shaw Ireland 1926 Grazia Deledda Italy 1932 John Galsworthy United Kingdom 1934 Luigi Pirandello Italy 1936 Eugene O'Neill United States 1948 T. S. Eliot United States/United Kingdom 1964 Jean-Paul Sartre (declined the prize) France 1969 Samuel Beckett Ireland 1986 Akinwande Oluwole Soyinka Nigeria 1997 Dario Fo Italy 2005 Harold Pinter United Kingdom
It's quite possible, though the Nobel Prize is usually given for an entire body of work or one's life work and many times not given until the body of work has proven it's value to society... so it might be many more years until that day.