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.
Photograph by Ryan Dausch