Use a peeler to thinly slice zucchini into “linguini” noodles. Set aside in a bowl and mix with salt. Let sit for 20 minutes to draw moisture out of the noodles. Drain the zucchini with a clean dish cloth or paper towels.
Heat olive oil in a large skillet. Add in chicken breast, salt, pepper, and garlic powder. Cook until no longer pink. Add in zucchini noodles, cherry tomatoes, and dried basil. Cook for an additional minute and remove from heat. Set aside in a bowl.
Heat olive oil for for the creamy sauce in the skillet. Add in garlic cloves and cook for about 30 seconds. Add in chicken broth to cool skillet, and reduce heat to low. (This step is important: if skillet is too hot, the Greek yogurt will curdle, so allow it to cool down before adding it in).
Add in Greek yogurt, parmesan, and dried basil. Mix until well combined. Add in the chicken, zoodles, and tomato mixture. Mix together and then remove from heat.
Serve and garnish with fresh chopped basil, as desired.