Sorry to say, Lisa, all Thai curries and most Thai food contains significant amounts of capsaicin. If you're deathly allergic, nothing would be safe because the wok which made your food may have been used for something spicy recently.

If you're somewhat tolerant, Thai meals are always served with rice, and you could order any of the dishes marked as mild on the menu and ask for it to be made mild. Some which come to mind are stir-fried veggies, beef in oyster sauce, somtham (papya salad), baked fish, fried rice, noodles like pot see hiew and "drunken" noodles, and desserts like coconut ice cream or mango with sticky rice.

You can try asking for no chili in Thai, but it may be embarrassing. That phrase is pronounced "my me prick". :-)