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Remove any giblets from the cavity of the chicken as well as any excess fat.
In a large bowl, combine the water and salt and stir with a wooden spoon until the salt crystals dissolve. Add the beer (it may foam up some, but it will settle down). Add the orange juice, lime juice, onion, garlic, hot sauce, and oregano and stir to combine.
Submerge the chicken in the brine or transfer to a large resealable plastic bag. (We like to double bag the chicken or set the bag in a separate bowl to contain leaks.) Refrigerate for 4 to 6 hours.
Remove the chicken from the brine and discard the brine. Wash the chicken inside and out under cold running water. Dry thoroughly with paper towels.
Tuck the orange and lime rinds in the main cavity. Oil the outside of the bird with the vegetable oil and dust with the Traeger Cajun Rub. Tuck the wingtips behind the back. Tie the legs together with butcher's string. (This gives you a moister bird and a more attractive presentation.)
When ready to cook, start the Traeger grill on Smoke with the lid open until the fire is established (4 to 5 minutes). Set the temperature to 350F and preheat, lid closed, for 10 to 15 minutes.
Place the chicken on the grill grate, breast-side up, and close the lid. Roast the chicken until an instant-read meat thermometer inserted into the thickest part of a thigh registers a temperature of 165F, 1-1/4 to 1-1/2 hours.
Remove the chicken to a platter and allow it to rest for 5 minutes. Untie the legs and carve. Enjoy!