Preheat the oven to 350 degrees F. Combine the cucumber, 1/4 teaspoon garam masala, 1/2 teaspoon salt and a few grinds of pepper in a medium bowl; toss to coat. Stir in the yogurt and set aside. Combine the chutney, chopped jalapeno, cilantro and lime juice in a separate bowl; stir to combine.
Season the chicken on both sides with the remaining 1 3/4 teaspoons garam masala and a generous pinch each of salt and pepper. Heat a large skillet over medium-high heat, then add the olive oil. Add the chicken and cook until browned, 4 to 5 minutes. Flip and cook until browned on the other side, 2 to 3 more minutes. Reduce the heat to medium and add 1/4 cup water. Cover and cook until the chicken is cooked through, 10 to 12 minutes. Transfer the chicken to a cutting board and let rest 5 minutes.
Meanwhile, warm the naan in the oven on a baking sheet. Slice the chicken and divide among the naan. Top with the chutney mixture, red onion, sliced jalapeno and more cilantro. Serve with the cucumber mixture.
Photograph by Ryan Dausch