I had always thought that the first American rodeo was held in Deer Trail, Colorado on Independence Day, 1869; and that the Lone Star version of rodeo was an imitation of the vaquero pastimes already well established by the Mexicans, who were the first to settle in Texas. Anyway, Hercules can surely wrangle!
Much of what Christian Soldier posted is true, so thank you for that correction to my previous post. I guess it all depends upon how you define the term "rodeo," as it was originally based on cattle herding techniques from Spain, which then were turned into informal events in the 1820s and 1830s in Mexico and the American southwest as the vaqueros and cowboys of that era competed to see who was best. These then emerged into the first "formal" rodeo which was held in Cheyenne, Wyoming in 1872. But, Prescott, Arizona has a claim with the first "professional" rodeo in 1888, when admission was charged and trophies were awarded. But, not a word about Texas. Thank-you again Christian Soldier for calling my attention to my previous post, so it could be corrected.