We successfully manipulated and observed carbon nanotubes (CNTs) in water, under an optical microscope. We employed a quenching observation method, where the intensity of fluorescent reagents around CNTs is decreased due to energy transfer. By this method, CNTs can be observed continuously for a long time by adding a new fluorescent reagent after fluorescence photobleaching. However, we must adjust the density of the fluorescent reagent around CNTs, which is extremely difficult to control. Thus, we built a fluorescent reagent supply system in a microfluidic chip. We found that polydimethylsiloxane with a porous structure could absorb the fluorescent reagent as a carrier and supply the reagent at a high and constant density for a long time. In experiments, using a microstirrer, we mixed two fluids uniformly, and succeeded in controlling the density of the fluorescent reagent. In addition, we applied dielectrophoretic (DEP) force for trapping the CNTs. The electrode material was indium-tin oxide, which is suitable for manipulation and observation of CNTs under an optical microscope because of its high conductive properties and good transparency. In these experiments, we trapped CNTs by DEP and observed CNTs by quenching on the chip, and confirmed that the fluorescent image of the CNTs was clearer than their bright-field images.