Long-term chemical weathering rates can now be measured in actively eroding landscapes using cosmogenic nuclide measurements of erosion in a geochemical mass balance of weathered soil and parent rock. We used the cosmogenic/mass balance method to measure long-term rates of chemical weathering and physical erosion at 43 locations that span a wide range of climates and denudation rates; mean annual temperatures range from 2 to 25 °C, average annual precipitation spans a 20-fold range (from 22 to 420 cm/yr), and denudation rates vary by 32-fold across our network of locations. Our results show that chemical weathering rates range from 0 to 173 t km-2 yr-1, in several cases exceeding the highest granitic weathering rates on record from previous work. We model the effects of temperature, precipitation and denudation rates with a simple, physically based expression that explains 89-95% of the variance in long-term chemical weathering rates. Our analysis shows that, for a given precipitation and temperature, chemical weathering rates increase proportionally with fresh-material supply rates. We refer to this as "supply-limited" weathering; fresh material is chemically depleted to roughly the same degree, regardless of its rate of supply from breakdown of rock. The temperature sensitivity of chemical weathering rates is 2 to 4 times smaller than what one would expect from laboratory measurements of activation energies for feldspar weathering and previous inter-comparisons of weathering rates from the field. Our results suggest that climate change feedbacks between temperature and silicate weathering rates may be weaker than previously thought, at least in actively eroding, unglaciated terrain. To the extent that chemical weathering rates are supply-limited in mountainous landscapes, factors that regulate rates of mineral supply from erosion, such as tectonic uplift, may lead to significant fluctuations in global climate over the long term.