Put the red peppers on the grill and char them until they are black on all sides. Put the peppers in a bowl and cover with plastic wrap. When cool enough to handle, scrape the charred black skin off the peppers and remove the stem and seeds. Coarsely chop and reserve. This can totally be done ahead.
Put the cumin, coriander, fennel and caraway in a dry saute pan and toast them until they become very aromatic. Grind all the spices into a coarse powder in a spice grinder.
Coarsely chop the dried chiles, toss them into the bowl of a food processor and pulse to pulverize. Add the toasted ground spices, the roasted red peppers, chopped garlic and tomato paste. Puree until the mixture is smooth. Add 1/4 cup of the olive oil and pulse to combine. Add in another 1/4 cup of olive oil and pulse again. Season with salt, to taste, if needed. Store in an airtight container.
Toss the chicken parts liberally with the harissa and let sit at room temperature up to 2 hours, or overnight or even a few days in the refrigerator.
Preheat the grill to medium.
Put the chicken on the grill and grill for 8 to 10 minutes on each side. You may have to move the chicken around, or flip it over a couple of times to prevent burning. You may also want to brush it a couple times with the leftover harissa, just remember it is pretty spicy! Remove the chicken from the grill and let it rest for 5 to 10 minutes before serving.
Make a big batch of this and it can live in the refrigerator for a long time and can be used for lots of different stuff.