Cook the chicken breasts and bacon: Heat a medium skillet and add the oil. When the oil is very hot, season the chicken breasts with salt and add them to the skillet. Cover and cook for 15 to 20 minutes, turning every 4 minutes until internal temperature reaches 165°F. Reduce the heat to medium-low if the chicken is browning too quickly. Remove the chicken from the skillet and place on a flat surface to rest. Pour the excess oil from the pan and add the bacon. Cook the bacon over medium heat until crispy, 5 to 8 minutes. Reserve the bacon grease. Keep the bacon and chicken warm.
Make the dressing: In the bowl of the food processor, blend the olive oil, almonds, mustard, red wine vinegar, and oregano. Add the reserved bacon grease. Taste for seasoning.
Assemble the salads: Cut the romaine into 1-inch slices and place one quarter on each of four plates. Slice the chicken and arrange a few slices in a row on top of each of the four plates. Make a row each of avocado, tomato and chopped egg with a drizzle of dressing. Add the warm bacon and sprinkle with the blue cheese and walnuts. Top with any remaining dressing. Serve immediately.
For a Fresh Twist: Salad can also be arranged on a serving platter. Place lettuce onto the center of a platter, arrange the chicken, avocado, tomatoes and egg in rows on either side of the lettuce. Sprinkle with bacon and blue cheese and drizzle with dressing.