What is the right way to connect a furnace flue pipe to an old chimney ?

Bought an old house with a gas furnace in the basement. The flue pipe is connected to the old chimney. There is no pipe or cap visible on top of the chimney and the pilot light keeps blowing out. Not an induced draft furnace. Good strong pilot light when it is lit.Should the flue pipe extend all the way to the top of the chimney?