Nope, you don’t. As the tri-suit won’t come off from the moment you start a race – either under a wetsuit or on its own if the water is warm enough – until you’ve crossed the finish line, so if you want to go commando you’re more than welcome!
It might feel strange at first, but you’ll soon get used to the skin-tight, stream-lined feel. No underwear also means no potential chafing in those delicate regions.
This will allow you to ride for longer and more often, with less uncomfortable niggles. Use chamois cream along the sensitive areas most prone to chafing to ensure the smoothest possible ride. Just ensure you wash your bib shorts or suit after each use to avoid build-up of bacteria, which can cause infection.
Female triathletes should wear a sports bra though, to protect delicate breast tissue while on the run section. Tri-suits will often have specific support built in, which can be quite handy as you can avoid spending the rest of the race in a soggy bra. However those with larger cup sizes might need the extra support of a good sports bra underneath.
So in short, no pants = no problem.