Chipboard is a recycled wood-and-cardboard substance that's sometimes used for floor underlayment instead of plywood. It's a fine underlayment if you're carpeting a room, but a big problem if you want to lay ceramic tile. Tiles need a very solid foundation that won't absorb moisture or move--two things that chipboard always does. The solution is to lay a very thick cement board over the chipboard, fastening it directly to the floor joists underneath.
Find and mark the floor joists under the chipboard, laying snaplines along the surface wherever there is a joist. You may be able to tell where the joists are by the pattern of nails in the chipboard, or you may have to measure from below the floor, in the basement, to figure it out. Once you find one, it's likely the rest will be 16 inches on centre from each other.
Use a circular saw to cut sheets of cement board so the edges of the sheets all meet at the lines you've marked for the joists. Spread carpenter's glue on the backs of the sheets and secure them with 2-inch wood screws every 6 inches along the joist lines. Sink additional 1 1/2-inch drywall screws throughout the rest of the surface, every 6 inches.
With your bucket and putty knife, mix a batch of thinset mortar. Get it to the consistency of a thin mud. Lay mesh drywall tape over the seams between the pieces of cement board. Spread the mortar along the seams with your putty knife, getting it as smooth and level as possible. Let it dry for a day.
Find the centre of the room and, with your snapline, divide it into four even squares. Working one square at a time, from the centre of the room, spread tile adhesive and lay your tiles, putting plastic spacers between them. Lay as many full tiles as will fit in the room, then let them set overnight.
Cut the tiles for the edges of the room using a platform tile cutter. Score each piece at the size needed, then press the prongs of the cutter down on either side of the mark to break it at the line. Install them with adhesive, making sure the cut side is facing the wall. Let them set for a day.
Pop out the plastic spacers with your putty knife. Mix powdered grout in a bucket with water, getting it to the consistency of heavy mud. Let it sit for 10 minutes, then spread it on the floor with a rubber trowel. Press it into the lines between the tiles, while squeezing it off the tile face. Work in sections, allowing the grout to sit on the floor for around three minutes. Wipe it down with a damp sponge to take up the excess grout and smooth out the grout lines. Let it dry 24 hours before using the floor.
Wear eye protection when using your circular saw and drill.