Combine the ketchup, soy sauce, packed brown sugar, olive oil, lemon juice, ground ginger, kosher salt, and black pepper in a large bowl or directly into a large zip-top bag and mix until smooth.
Add the thin-sliced chicken breasts to the bag with the marinade, seal, and press or massage to coat the chicken evenly; refrigerate for at least 30 minutes or up to overnight.
When ready to cook, lightly oil the grill grates and preheat your grill to medium-high heat (or heat an indoor grill pan over medium-high).
Remove the chicken from the marinade, placing the used marinade bag aside, then dunk the pineapple spears into the remaining marinade in the bag to lightly coat and place them on the grill; discard the marinade bag.
Grill the chicken for about 5 minutes with the lid closed, flip, and grill 4 to 5 more minutes with the lid closed, or until an instant-read thermometer inserted into the thickest part reads 165°F (74°C).
Grill the pineapple spears, turning every 2 to 3 minutes so all sides get grill marks and heat through; total time will be similar to the chicken.
Transfer chicken and pineapple to a platter, garnish with thinly sliced green onions if desired, and serve immediately.