Heat a large skillet over medium heat. Add the red onions, orange peppers, red peppers, oregano and 1/2 teaspoon salt and cook, stirring often, until the vegetables are soft and have a touch of color, about 9 minutes. Add the capers and balsamic; reduce the heat to low and cook an additional 5 minutes, until the peppers are coated in the vinegar. Stir in the basil and set aside to cool.
Preheat a panini press. Halve the ciabatta rolls horizontally and scoop out some of the insides from the top halves. Divide the pepper mixture evenly among all the halves and top each half with a slice of provolone. Divide the sliced chicken among the ciabatta bottoms and then cover with the ciabatta tops, pressing down slightly. Brush the outside of each sandwich with olive oil.
Place the sandwiches in the panini press, close the top, and cook until warmed through and the cheese is melted, about 3 minutes.