Make these hearty wraps for sack lunches or picnics. Lettuce, avocado, and cucumber freshen the taste of the Mexican-sauced chicken.
In large deep skillet, heat oil over medium-high heat. Add chicken and onion; sauté until chicken is lightly colored and onion is softened, 5 to 7 minutes. Add tomatoes with their juice, cumin and 1/2 teaspoon salt. Bring to boiling; cook, uncovered, stirring occasionally, until thickened and most of liquid has evaporated, about 20 minutes. Remove from heat. (Mixture can be made ahead and refrigerated, and then brought to room temperature before proceeding.)
Halve avocados; remove pit; peel. Cut lengthwise in 1/4-inch-thick slices. In small bowl, toss avocado with 1 tablespoon lime juice and 1/4 teaspoon salt. Halve cucumber crosswise, then halve lengthwise; seed. Cut pieces into thin lengthwise slices. In bowl, toss with remaining 1 tablespoon lime juice and 1/4 teaspoon salt.
On work surface, spread out 1 tortilla. Cut off 1 inch from edge of each tortilla. Arrange tortilla, cut side away from you. Spread one-fourth of chicken mixture, about 1 cup, across lower fourth of tortilla, about 1 inch from bottom. Top chicken mixture with 2 lettuce leaves, one fourth of the avocado and one-fourth of the cucumber strips. From bottom edge, tightly roll up tortilla. Arrange, cut edge down, on work surface; slice diagonally in half. Repeat with remaining tortillas and fillings. (Wraps can be made up to 6 hours ahead and individually wrapped in plastic, and then refrigerated. For best flavor, serve at room temperature.)