Preheat the oven to 350˚. Trim the stem end of the squash and poke holes 1/2 inch deep all over the squash with a paring knife; put in a heatproof glass bowl. Microwave, turning the squash halfway through, until tender when pierced with a fork, about 14 minutes. Set aside until cool enough to handle, then halve lengthwise and scoop out the seeds. Scrape the flesh into strands with a fork.
Rub the chicken with 1 tablespoon olive oil, 2 teaspoons coriander and the thyme. Season generously with salt and pepper. Heat the remaining 1 tablespoon olive oil in a large ovenproof nonstick skillet over medium-high heat. Add the chicken and cook until browned on the bottom, about 3 minutes. Flip the chicken, transfer the skillet to the oven and bake until cooked through, about 13 minutes. Remove the chicken to a cutting board to rest.
Return the skillet with its juices to medium-high heat and add the squash and remaining 1/2 teaspoon coriander. Cook, stirring occasionally, until the squash has absorbed the juices, 3 to 5 minutes. Season with salt and pepper. Divide among plates.
Combine the pears, lime juice, pomegranate seeds, mint and pistachios in a bowl. Slice the chicken and serve with the squash. Spoon the pear mixture on top.