Chipotle does not have a gluten free menu but instead has a list of gluten-containing ingredients to avoid. Cross-contamination is a concern, however, so let the person taking your order know that you are gluten free and if you need them to take the proper precautions.
From their website: "If you avoid gluten, don't eat our flour tortillas. If you are highly sensitive to gluten and would like us to change our gloves, just let us know at the start of your order. You should be aware items containing corn, including corn tortillas (chips, soft corn, and crispy corn tortillas) and corn salsa, may have a small amount of gluten from potentially co-mingling with gluten-containing grains in the field."
Everything on Chipotle's menu is gluten free, except for their flour tortilla. All of their meat is safe, as well as all of their add-ins. When I go, I ask for them to change gloves, and they are always friendly about it.
I usually get hard tacos or a bowl, so they prep everything in the clean bowl, not on contaminated surfaces. I have never had any cross contamination issues.