The present invention relates to a dripless chimney cap which prevents condensates from dripping down the outside of a chimney. The dripless chimney cap includes a cone-shaped top cap at the top of the chimney cap for stopping liquids and objects from falling into the chimney. A condensation drip pan in the shape of an inverted cone is positioned below the top cap and functions to catch and collect condensates, directing them toward the inside of the chimney flue. A mounting flange attaches to the chimney and secures the condensation drip pan and top cap to the chimney. A screen mesh located between the condensation drip pan and the mounting flange is designed to allow cross air flow.