  We generalize Chirka's theorem on the extension of functions holomorphic in a
neighbourhood of graph(F)\cup(\partial D\times D) -- where D is the open unit
disc and graph(F) denotes the graph of a continuous D-valued function F -- to
the bidisc. We extend holomorphic functions by applying the Kontinuitaetssatz
to certain continuous families of analytic annuli, which is a procedure suited
to configurations not covered by Chirka's theorem.
