First, make sure you know which organization sanctions the event you are interested in. There are at least two organizations that sanction triathlons. One, the International Triathlon Union, explicitly forbids running barefoot (http://www.triathlon.org/uploads/docs/itusport_competition-rules-2013_final.pdf). The other, USA Track & Field states that runners "may compete in bare feet or with footwear on one or both feet" (http://www.usatf.org/About/Competition-Rules.aspx). In addition, the race officials organizing an event may set additional rules for their specific event. I competed in the Life Time Fitness triathlon in Minneapolis last year. Although the event was sanctioned by USATF, I never got a firm statement that I could run without shoes. Considering the amount of effort I put into preparation, I chose to run with shoes, rather than risk a disqualification.