Most commercial teriyaki products have gluten because soy sauce is often made with wheat. We use La Choy which does not use wheat. The only problem I have with La Choy is that it's not as natural as other soy sauces - it has corn syrup and caramel color to make up for the wheat but it is cheap where other gluten free varieties are not. We use a lot of soy sauce so I hate to pay $4 for a little bottle when La Choy is about $2 and is a decent sized bottle (we used to buy it by the half gallon but have yet to find a gluten free bottle that size).
I wanted teriyaki chicken and came up with a fairly simple recipe. I used this as a marinade for my chicken so it does not have a thickener. After marinating the chicken I boiled it down and it was a fine sauce. If you want it as a sauce exclusively you will need to add cornstarch to it before cooking.
*note - I made this up as I went along and did not measure so use your own judgment but this is pretty close.
1 20oz can crushed pineapple
1/4 cup brown sugar
2 teaspoons minced garlic
2 teaspoons minced ginger
1/2 cup soy sauce
Puree pineapple in blender until it's the consistency of a smoothie. Pour into sauce pan and add remaining ingredients. Heat over med heat to melt sugar and to give all the flavors a chance to blend. I cooked it over low heat for about 30 minutes while prepared the chicken. Pour over raw chicken and marinate 2-4 hours. Bake chicken at 350 until cooked fully. Heat remaining marinade in saucepan until boiling, boil a few minutes or reduce to low and let cook while chicken is cooking.