Preheat oven to 350 degrees F.
Mix together mochiko, sugar, coconut milk, water, and extract (if using) in a large bowl, making sure no dry lumps of mochiko remain.
Separate mochi batter into thirds.
Add 1-2 drops green food coloring to one third and 1-2 drops pink or red food coloring to another third. Leave remaining third white.
Pour the green mochi batter into a well greased 9x13” pan (I recommend Pyrex so it doesn’t stick).
Bake uncovered for 15 minutes, or until the layer is set.
Carefully pour white mochi batter on top of baked green layer.
Return to oven and bake again for another 15 minutes or until set.
Carefully pour pink mochi batter on top of the white.
Cover entire dish tightly with foil and bake for 30 minutes or until mochi is cooked through.
Uncover mochi and let cool down to room temperature.
Turn out the mochi onto a surface dusted with katakuriko and slice into rectangles (use a plastic knife or pizza cutter to prevent mochi from sticking to the knife). Continue dusting with katakuriko as needed to prevent sticking.
Leftover chi chi dango can be saved in an airtight container at room temperature for a few days.