In the McMurdo Dry Valleys, Antarctica, dilute glacial meltwater flows down well‐established streambeds to closed basin lakes during the austral summer. During the 6–12 week flow season, a hyporheic zone develops in the saturated sediment adjacent to the streams. Longer Dry Valley streams have higher concentrations of major ions than shorter streams. The longitudinal increases in Si and K suggest that primary weathering contributes to the downstream solute increase. The hypothesis that weathering reactions in the hyporheic zone control stream chemistry was tested by modeling the downstream increase in solute concentration in von Guerard Stream in Taylor Valley. The average rates of solute supplied from these sources over the 5.2 km length of the stream were 6.1 × 10⁻⁹ mol Si L⁻¹ m⁻¹ and 3.7 × 10⁻⁹ mol K L⁻¹ m⁻¹, yielding annual dissolved Si loads of 0.02–1.30 mol Si m⁻² of watershed land surface. Silicate minerals in streambed sediment were analyzed to determine the representative surface area of minerals in the hyporheic zone subject to primary weathering. Two strategies were evaluated to compute sediment surface area normalized weathering rates. The first applies a best linear fit to synoptic data in order to calculate a constant downstream solute concentration gradient, dC/dx (constant weathering rate contribution, CRC method); the second uses a transient storage model to simulate dC/dx, representing both hyporheic exchange and chemical weathering (hydrologic exchange, HE method). Geometric surface area normalized dissolution rates of the silicate minerals in the stream ranged from 0.6 × 10⁻¹² mol Si m⁻² s⁻¹ to 4.5 × 10⁻¹² mol Si m⁻² s⁻¹ and 0.4 × 10⁻¹² mol K m⁻² s⁻¹to 1.9 × 10⁻¹² mol K m⁻² s⁻¹. These values are an order of magnitude lower than geometric surface area normalized weathering rates determined in laboratory studies and are an order of magnitude greater than geometric surface area normalized weathering rates determined in a warmer, wetter setting in temperate basins, despite the cold temperatures, lack of precipitation and lack of organic material. These results suggest that the continuous saturation and rapid flushing of the sediment due to hyporheic exchange facilitates weathering in Dry Valley streams.