1. Mix cream cheese and chutney in a food processor until smooth. Add pepper to taste.
2. Spread a thin layer of cream cheese to the edge of each tortilla. Top each with 2 lettuce leaves. Divide sliced turkey among the tortillas; layer each tortilla equally with cucumber and tomato.
3. Tightly roll up; wrap in damp paper towels and refrigerate several hours. To serve, cut each roll-up into 5 pieces.