Can you do tie dye t-shirts without chemicals?

Use vegetable dyes instead.

Here's how to do it: http://www.nymetroparents.com/article/instructions-to-tie-dye-t-shirts-with-food-coloring

It looks like the colors may turn out lighter - but that might just be the amount of food coloring they used.

HTH

Looks like food coloring can be used as Linda stated. The instructions have you soak the shirts in vinegar. (kinda like making egg dye colors more vibrant). Then it talks about mixing the foodcoloring with water. I'd imagine you can use more or less coloring or more or less water to darken or lighten.

I also saw some talk of using koolaid instead of foodcoloring

Kool aid

fruit and vegetable drinks let it soak

There is a way to Tie dye using Tumeric for a bright yellow pattern, saw the directions on HomeTalk.