In a large mixing bowl stir together the soy sauce, brown sugar, beer, pineapple juice, tomato paste, vinegar, ginger, and garlic. Remove 1/3 cup of the mixture, cover, and set aside.
Sprinkle the chicken on all sides with salt.
Add the chicken to the mixing bowl with the marinade (or add it all to a large ziplock bag), cover, and refrigerate for at least 1 hour and up to 6.
Preheat the grill to medium-high.
Add the chicken and pineapple.
Brush the chicken with the reserved 1/3 cup marinade and turn every few minutes until cooked through about 8 minutes.
Remove the chicken and pineapple from the grill, add to a serving platter.
Sprinkle with green onions.