Preheat the oven to 400°F (200°C) and line a rimmed baking sheet with aluminum foil.
Cut the spaghetti squash in half lengthwise and scoop out the seeds.
Rub the cut sides of the squash with 1/2 tablespoon of oil and sprinkle with salt, then place cut-side down on the prepared baking sheet.
Bake the squash until fork-tender, about 45 to 60 minutes. Remove from oven and let cool slightly.
While the squash bakes, heat the remaining 1/2 tablespoon oil in a large skillet over medium heat.
Season the cubed chicken with a pinch of salt, garlic powder, and onion powder.
Cook the chicken in the skillet in a single layer for 5–7 minutes, stirring occasionally, until golden and cooked through (165°F internal temperature). Transfer to a plate and set aside.
Spread the pine nuts on a small baking sheet and toast in the oven until just golden, about 5–10 minutes; watch closely to avoid burning.
Place toasted pine nuts in a food processor and pulse until crushed. Add basil, lemon juice, minced garlic, 1/2 teaspoon salt, and pulse to combine.
With the processor running, stream in the 2 tablespoons olive oil until the pesto is smooth and emulsified; scrape sides as needed.
Use a fork to shred the baked spaghetti squash flesh into strands and divide the squash between two bowls.
Toss half of the pesto into each bowl of squash, mix to coat, then top with the cooked chicken. Taste and add more salt if needed.
Serve immediately.