Photon absorption by carbon nanotubes creates bound electron-hole pairs called excitons(1-8), which can exist in spin-polarized triplet or spin-unpolarized singlet configurations. Triplet excitons are optically inactive owing to the weak spin-orbit coupling in nanotubes. This prevents the optical injection of electron spin into nanotubes for spintronic applications(9) and limits the efficiency of photocurrent generation(10). Here, we show that it is possible to optically excite the triplet exciton by using a ferromagnetic semiconductor as a spin filter(11) to mix the singlet and triplet excitons. The triplet contribution to the photocurrent is detected, representing the first direct evidence of the triplet exciton in carbon nanotubes.