Abstract: It is well known that there exist domains in C^n, n>1, such that all functions holomorphic therein extend holomorphically past the boundary. In this talk, we shall examine this phenomenon for certain refinements of the fundamental example of Hartogs. We shall look at a generalization of Hartogs' construction discovered by E .M. Chirka. Finally, we shall provide a partial answer to a related question raised by Chirka. There will be plenty of pictures, and very little familiarity with several complex variables will be required.