Cook the bacon in a medium nonstick skillet over medium heat, turning once, until crisp, about 8 minutes. Remove the bacon to a paper towel¿lined plate to drain. Let cool slightly, then crumble.
Meanwhile, fill a medium bowl with ice water. Bring a medium saucepan of water to a boil and add the eggs; cook 4 minutes, then remove 2 eggs with a slotted spoon and transfer to the ice water. Continue cooking the remaining 2 eggs until hard-boiled, 6 more minutes; drain and let cool.
Make the dressing: Remove the eggs from the ice water and peel; transfer to a blender. Add the vegetable oil, vinegar, dill, 1/2 teaspoon salt and a few grinds of pepper and puree until smooth.
Put the romaine in a large serving bowl and drizzle with the dressing. Peel and slice the hard-boiled eggs. Arrange the avocado, chicken, feta, tomatoes, eggs and bacon in rows over the salad. Top with the pita chips and more dill. Toss before serving.