Bring a pot of water to a gentle boil on the stove. Place a chicken breast in the boiling water and cook until it is no longer pink inside. Remove and allow to cool, then shred into bite-sized pieces.
Wash all of your vegetables. Chop the cabbage, mint, cilantro, and Thai basil coarsely. Slice the carrots and cucumbers into bite-sized thin strips.
Prepare the salad dressing by mixing the satay peanut sauce, vinegar, sugar, grated ginger, and lime juice. Set aside to allow the flavors to meld.
Assemble the salad by tossing all ingredients in a bowl and pouring as much peanut sauce dressing as you like over it. Garnish with a slice of lime and enjoy!