Remove the flue tile from the chimney with a masonry hammer. Crack the tile by striking it on the side. Remove the tile pieces by hand until the entire tile section is removed.
Mix masonry grade cement mortar in a five gallon bucket using a hand trowel.
Apply the cement mortar to the top of the flue section below the flue piece you just removed. About an inch of mortar is necessary to set the new flue tile in place.
Slide the new flue tile (which is a rectangular, tube-shaped section of clay flue) into the chimney and set it so the bottom edge is on top of the mortared flue tile. Tap the flue tile into place with the masonry hammer to settle the tile into the mortar.
Scrape the remaining overflow cement mortar from the sides of the tile with the trowel. Allow the mortar to dry for six to 10 hours. Check the flue tile again to ensure it is setting properly.