Cook chiles in a skillet over high heat 5 minutes or until fragrant, turning often. Remove stems and seeds from chiles. Place chiles in a large bowl; add 4 cups boiling water, and let stand 20 minutes. Drain.
Process chiles, vinegar, next 8 ingredients, and 3/4 tsp. salt in a blender or food processor until smooth, stopping to scrape down sides as needed.
Sprinkle pepper and remaining 2 1/4 tsp. salt over brisket. Place brisket in an extra-large zip-top plastic freezer bag or a large shallow dish. Pour chile mixture over brisket; rub brisket with chile mixture. Seal or cover, and chill 2 to 24 hours.
Soak wood chips in water 30 minutes. Prepare gas grill by removing cooking grate from 1 side of grill. Close grill lid, and light side of grill without cooking grate, leaving other side unlit. Preheat grill to 250° to 300° (low) heat.
Spread 4 cups soaked and drained wood chips on a large sheet of heavy-duty aluminum foil. Cover with another sheet of heavy-duty foil, and fold edges to seal. Poke several holes in top of pouch with a fork. Place pouch directly on lit side of grill. Cover with cooking grate.
Remove brisket from marinade, discarding marinade. Place brisket, fat side up, in a 12- x 10-inch disposable foil roasting pan. Place pan on unlit side of grill; cover with grill lid.
Grill brisket, maintaining internal temperature of grill between 225° and 250°, for 1 1/2 hours. Carefully tear open foil pouch with tongs, and add remaining 4 cups soaked and drained wood chips to pouch.
Cover with grill lid, and grill, maintaining internal temperature of grill between 225° and 250°, until a meat thermometer inserted into thickest portion of brisket registers 165° (about 1 1/2 hours).
Remove brisket from grill. Place brisket on a large sheet of heavy-duty aluminum foil, and pour 1/2 cup pan drippings over brisket; wrap with foil, sealing edges.
Return brisket to unlit side of grill, and grill, covered with grill lid, until meat thermometer registers 195° (about 2 hours). Remove from grill, and let stand 10 minutes. Cut brisket across the grain into thin slices. Squeeze juice from limes over brisket before serving. Garnish, if desired.
Note: Guajillo chiles and Mexican oregano may be found on the spice aisle of specialty grocery stores or in Mexican markets.
*Dried oregano may be substituted for Mexican oregano.
Oven-Roasted Fiesta Brisket: Prepare recipe as directed through Step Preheat oven to 350°. Remove brisket from marinade, discarding marinade. Wrap brisket with heavy-duty aluminum foil, and place in a jelly-roll pan. Bake 3 hours or until a meat thermometer inserted into thickest portion registers 195° and brisket is very tender. Remove from oven, and let stand 10 minutes. Cut brisket across the grain into thin slices. Prep: 30 min., Cook: 5 min., Stand: 30 min., Chill: 2 hr., Bake: 3 hr.