Heat grapeseed oil in a large saucepan (that has a lid, for later) over medium-high heat.
Season chicken with salt and pepper (generously!). Brown chicken pieces all over by placing chicken pieces in pan skin side down first, browning, then turning over. It will take about 10 minutes. Transfer chicken to a plate and set aside.
Turn down heat under saucepan to medium. Add garlic, onions, rosemary, and oregano to pan and cook until onions are translucent, about 5 minutes. Add carrots and bell peppers and cook until the vegetables are starting to soften, about 5 minutes.
Add wine and stir to scrape up browned bits from bottom of the saucepan. Turn up heat if necessary to bring wine to a simmer. Add tomatoes to the pan and stir. Taste and season; you will need to add about a teaspoon of salt and 5 - 6 turns on a pepper mill. Bring to a boil, then turn the heat down to simmer.
Place chicken pieces back into pan skin side up in the sauce, and pour any juices from the plate into the saucepan. Cover the sauce pan with a lid, with a little space for steam to escape. Cook until chicken is tender, about 40 minutes. Every once in a while, check inside and if there isn't enough braising liquid, add a little bit of water or light chicken stock.
You can transfer the chicken and sauce to a serving platter with high-ish sides or serve it right from the pan. Garnish with chopped parsley and basil. I served my Chicken Cacciatore with steamed quinoa.