Magma ascent rates control volcanic eruption styles. However, the rates at which basaltic magmas ascend through the crust remain highly uncertain. Although recent studies have successfully exploited records of decompression driven degassing to estimate the rates at which H2O-rich basalts ascend, such approaches cannot readily be applied to primitive and H2O-poor basalts that erupt in ocean island and mid-ocean ridge settings. Here we present magma ascent rates obtained by modeling the dissolution of clinopyroxene crystals in a wehrlitic nodule from the primitive Borgarhraun lava flow in North Iceland. High-Al2O3 clinopyroxene core compositions are consistent with crystallization near the Moho (~800 MPa), whereas low-Al2O3 clinopyroxene rims and inclusion compositions are consistent with crystallization at or near the surface. We interpret low-Al2O3 rims and inclusions as the crystallized remnants of boundary layers formed by the dissolution of high-Al2O3 clinopyroxene during magma ascent. By combining characteristic rim dissolution lengths of 50–100 μm with published experimental calibrations of clinopyroxene dissolution behavior, we estimate that the Borgarhraun magma most likely decompressed and ascended at rates of 3.0–15 kPa.s−1 and 0.11–0.53 m.s−1, respectively. These rates are slightly faster than published estimates obtained by modeling the diffusive re-equilibration of olivine crystals, suggesting that the Borgarhraun magma either accelerated upwards or that it stalled briefly at depth prior to final ascent. Comparisons with other basaltic eruptions indicate that the H2O-poor magma that fed the dominantly effusive Borgarhraun eruption ascended at a similar rate to some H2O-rich magmas that have fed explosive eruptions in arc settings. Thus, magma ascent rates do not appear to correlate simply with magma H2O contents. Overall, our findings confirm that primitive and H2O-poor basalts can traverse the crust within days, and may erupt with little precursory warning of magma ascent.