A Delaware Cooperative Extension colleague recently provided this answer to a similar question about eradicating Chameleon plant.
Houttuynia cordata 'Chameleon' is a medium-sized herbaceous perennial ground cover that spreads vigorously underground by fleshy rhizomes. The plant is invasive and extremely difficult to eliminate from the landscape.
A combination of digging and spraying with a garden herbicide that contains the active ingredient glyphosate will work eventually. A commonly known herbicide containing glyphosate is Roundup; other mixtures containing glyphosate are available. When digging a small patch be careful to get all of the roots. The roots tend to break off and re-sprout. August is the best time to spray this plant. It may be necessary to spray several times as the plant re-sprouts.
It is not too late to begin spraying this plant with glyphosate. Be careful to protect desirable plants that are nearby. Glyphosate is a broad spectrum herbicide that will harm any plant with which it comes in contact. Be sure to use this product according to the directions on the label and follow the personal protection directions that you will find there as well.