In a medium saucepan poach chicken with a pinch of salt and enough water to cover. Bring to a boil then reduce to a simmer and cook, covered, until cooked through about 10 minutes. Remove from heat then drain water and shred or chop chicken, set aside.
In a food processor combine dill, walnuts, and garlic. Pulse until well combined. With the motor running slowly add the olive oil, pulse until combined.
Transfer pesto to a large bowl, add chicken, red onion, lemon juice and zest, salt and pepper to taste. Add vinegar. Toast bread and divide chicken among slices top with romaine. Enjoy!