Mix either a citrus-based degreaser or a petroleum-based cleaner with water in accordance with the cleaner's instructions. Either one can help remove tar from both shingles and a chimney.
Place a scraper under any larger globs of tar and scrape it up off the shingles or the chimney. Use particular care with the shingles to avoid tearing them up accidentally while removing the tar.
Dip a cloth into the cleaning solution and then squeeze it over the tar stains to get the cleaner into them. Let the cleaner sit for several minutes to give it time to break up the tar. Wear rubber gloves to prevent skin exposure.
Dip a scrub brush into the solution and then scrub it back and forth over the tar stains. Rinse the chimney or the shingles with regular water once the tar is removed.