To medium-sized saucepan, add chicken breast, lemon slices, parsley, garlic clove, and onion and cover with cold water by about 1 inch . Heat on medium high, covered. Without disturbing chicken, stir water in pan gently once or twice to make sure temperature is even throughout. Reduce heat to low simmer and cook, uncovered, at a gentle simmer for 10 minutes. Chicken should be cooked to an internal temperature of 165 F . Remove chicken from water and allow to cool. Cover and refrigerate for 1 to 2 hours or leave overnight.
To make arugula yogurt dressing, into bowl of food processor, place 2 cups arugula, yogurt, salt, pepper, lemon zest, and goat cheese. Blitz until smooth.
To make chicken salad, dice chicken finely and combine with 1/4 cup dressing, celery, chives, and walnuts.
To serve, toast a piece of sourdough bread, spread a little arugula dressing onto bread. Top with about 1/4 cup fresh arugula and a scoop of chicken salad. Eat open faced or top with another piece of bread to make a sandwich.