Start by preparing all your components so assembly goes smoothly. If your eggs aren't already hard-boiled, boil them now and let them cool completely before chopping finely. Shred your cooked chicken into bite-sized pieces, dice the tomato into small ¼-inch pieces, finely dice the celery, thinly slice the cucumber into ⅛-inch rounds, and freshly chop the parsley. Grate or finely chop the sharp cheddar cheese. Having everything prepped and ready will make the next steps quick and efficient.
In a large mixing bowl, combine the shredded chicken, finely chopped hard-boiled eggs, cheese, diced tomato, and fresh parsley. Toss these ingredients together gently to distribute them evenly throughout. I like to fold everything together rather than stir aggressively—this keeps the chicken from breaking apart too much and maintains a nice texture in the final salad.
In a small bowl, whisk together the mayonnaise, ranch dressing, lemon juice, salt, and pepper until well combined. Pour this mixture over the chicken salad base from Step 2 and fold everything together until the chicken salad is evenly coated and creamy. I find that folding rather than stirring vigorously keeps the texture lighter and prevents everything from becoming mushy. Taste and adjust seasoning if needed.
Place your crackers on a serving platter or individual plates. Spoon approximately 1 tablespoon of the chicken salad mixture onto each cracker, then top with a single thin slice of cucumber. Arrange the crackers on a platter and serve immediately while the crackers are still crisp. The cool, creamy chicken salad pairs beautifully with the buttery crunch of the Ritz crackers and the refreshing cucumber slice.