As long as you phrase your dietary questions in the positive ("Is the green curry gluten free?"), you will learn what you need about this fairly authentic Thai menu. I am also soy intolerant, but the server knew how to narrow down my choices, because there is more soy and soy sauce than I came across in Thailand. We will include Chada Thai in our future drives past Palm Springs. It is worth a cut through the edge of town where I-10 curves around Palm Springs.
He said everything was gluten free. Not sure about that but it was a really good meal with generous portions and great price.
Cheap! And beautiful delicious gluten free curries, pad thai, tea, and the Tom Kah is the best I've ever had. Love this Thai restaurant.