I agree--especially if you brine--but even if you don't there's way too much salt and sugar in the BRITU for chicken.
Thyme is a good starting point though. Lemon zest is a nice addition if you're doing a low/slow. For a high-heat cook I'd suggest making lemon zest part of the baste, brine, or marinade, instead of the rub.
Thyme works well with onion and garlic, obviously, but also works very well with ground dried chilies, cinnamon, allspice, coriander, cumin, ground dried sweet fruits (like apple and cherry), ginger, many of the 'exotics', among others--a whole host of spices--so there are lots of combo possibilities. Be careful with rosemary and fowl. Like bay, it works well, but too much is easily overpowering. Also like bay, it must be ground to a powder if using in a rub as in its dry state it is sharp and does not soften appreciably with cooking. Both are also very suitable for the brine or marinade layer of flavoring. In any case (brine or marinade or rub, bay or rosemary) be sparing till you see what amount it (or they) need to work best with what else you have planned.