The 1980 encounter by the Voyager 1 spacecraft with Titan, Saturn's largest moon, revealed the presence of a thick atmosphere containing nitrogen and methane (1.4 and approximately 0.05 bar, respectively). Methane was found to be nearly saturated at Titan's tropopause, which, with other considerations, led to the hypothesis that Titan might experience a methane analogue of Earth's vigorous hydrological cycle, with clouds, rain and seas. Yet recent analyses of Voyager data indicate large areas of super-saturated methane, more indicative of dry and stagnant conditions. A resolution to this apparent contradiction requires observations of Titan's lower atmosphere, which was hidden from the Voyager cameras by the photochemical haze (or smog) in Titan's stratosphere. Here we report near-infrared spectroscopic observations of Titan within four narrow spectral windows where the moon's atmosphere is ostensibly transparent. We detect pronounced flux enhancements that indicate the presence of reflective methane condensation clouds in the troposphere. These clouds occur at a relatively low altitude (15+/-10 km), at low latitudes, and appear to cover approximately 9 per cent of Titan's disk.