In a small bowl, mix together all the marinade ingredients.
Light a charcoal fire and let it burn until the charcoal is covered with white ash (and about medium hot); bank half the coals to one side of the grill, half to the other. Or, heat a gas grill: You’ll need a grill with three burners, so that you can turn heat the outer two to medium and leave the center one off.
While the grill is heating, remove the giblets (if there are any) from the cavity of the chicken. Flip the chicken onto its breast. Using poultry shears, cut down through the backbone from tail to neck, staying as near as possible to the center of the bone (to keep the skin attached). If you don’t have shears, lay the bird on its back, insert a long heavy knife into the body cavity and press down hard with a rocking motion to cut through the length of the backbone. Open the bird out onto your work surface, breast side up. Make sure that the legs are turned inward. Using your fist or a mallet, wallop the bird on the breast—hard enough to dislodge the center bones and flatten out the breast. Twist the last joint of the wings up over the breast and then down behind the “shoulders,” tucking them in firmly to keep them in place during grilling.
Smear both sides of the chicken with the marinade. Lay in the center of the grill (it will not be over direct heat). Cook without turning, basting from time to time with any remaining marinade, until the juices run clear when a thigh is pierced deeply with a fork (an instant-read thermometer should register about 160 degrees when inserted at the thickest part of the thigh), about 30 minutes at 500 degrees.
While the chicken is grilling combine stock, black pepper, oregano, and beer in a small saucepan and simmer for about 10 minutes.
Remove the chicken to a cutting board. It will lose less juice is you cover it loosely with foil and let it rest 5 or 10 minutes. Cut into quarters (or smaller pieces). Transfer a portion to each of 4 dinner plates. Top with the jus and you’re ready to serve.