Preheat a grill or grill pan over medium-high heat (about 425°F).
Pound the chicken breasts to an even thickness using the flat side of a meat mallet or rolling pin.
Brush both sides of the chicken lightly with about 1 Tbsp olive oil and season with salt and freshly ground black pepper.
Lightly oil the grill grates or grill pan, then grill the chicken, turning once halfway through, until an instant-read thermometer inserted into the center reads 165°F, about 6–8 minutes total depending on thickness.
Transfer the chicken to a plate, tent with foil and let rest for 10 minutes, then dice into bite-sized cubes.
Place the diced chicken in a bowl, pour the 6 Tbsp Greek vinaigrette over it and toss to coat evenly.
To assemble each wrap, spread about 3 Tbsp hummus over a tortilla, then top with dressed chicken, chopped romaine, diced tomatoes, diced cucumber and crumbled feta.
Fold or roll the tortilla to enclose the filling and serve immediately.