Fill a pressure washer with mild house detergent. Eco-friendly cleaning solutions intended for use in conjunction with pressure washers are available at hardware stores and home improvement centers.
Wear protective eyewear and dispense the cleaner according to the manufacturer's instructions. Be sure to evenly distribute the solution so that all of the chalking paint has been coated.
Allow the soap to soak the surface of the house for 10 to 15 minutes before rinsing it thoroughly. Maintain the water pressure at 1500-2000 psi until the surface is completely free of soap residue.
Wait for the house to dry for a full 24 hours before applying a new coat of paint. You can attempt to scrub excess chalky residue with a chemical solvent, but some should be expected to remain.
Apply a quality paint primer in preparation for a new coat. Acrylic primer will produce the best results for house paint with remaining chalk.