Put the chicken in a medium (about 3-quart capacity) baking dish.
Mix the marinade
Whisk together the mustard, tomato paste, lemon juice, olive oil, thyme, garlic, salt, pepper, and chili in a medium bowl.
Assemble and bake the chicken
Pour the marinade over the chicken and turn the pieces over to coat. Scatter the shallots over the chicken, poking them in between the thighs here and there. Some of the unexposed shallots will crisp and brown, while the covered pieces will bake and soften.
You can bake the chicken immediately or cover and refrigerate the chicken and marinade up to 24 hours ahead.
Bake the chicken 25-30 minutes, until the chicken is opaque and the juices are bubbling. Serve warm.
Make ahead: Marinate the chicken overnight in the mustard mixture and simply pop in the oven when you're ready to cook dinner.
Freeze the unbaked chicken in a freezer-safe bag. Thaw overnight in the fridge and bake.
Substitute fresh thyme with another fresh aromatic herb like rosemary or oregano. Dried herbs will work too, just reduce the amount by half.