Some have argued that naked hoplites depicted in sculpture and other forms of art are representative of heroic nudity and do not reflect actual practice. But it is certainly possible, as the Greeks competed in athletics in the nude as well as other strenuous activities. Only around 10% of hoplites had bronze cuirasses, a greater number used linothorax type armour although the proportion would have probably varied depending upon the wealth of individual hoplites (maybe 20-30%?). The majority of hoplites would have relied on their shields alone for protection, so it would be up to you to decide what percentage would forego wearing a chiton and fight naked