The published literature debates the extent to which naturally occurring stratospheric ozone intrusions reach the surface and contribute to exceedances of the U.S. National Ambient Air Quality Standard (NAAQS) for ground-level ozone (75 ppbv implemented in 2008). Analysis of ozonesondes, lidar, and surface measurements over the western U.S. from April to June 2010 show that a global high-resolution (∼50 × 50 km2) chemistry-climate model (GFDL AM3) captures the observed layered features and sharp ozone gradients of deep stratospheric intrusions, representing a major improvement over previous chemical transport models. Thirteen intrusions enhanced total daily maximum 8-h average (MDA8) ozone to ∼70–86 ppbv at surface sites. With a stratospheric ozone tracer defined relative to a dynamically varying tropopause, we find that stratospheric intrusions can episodically increase surface MDA8 ozone by 20–40 ppbv (all model estimates are bias corrected), including on days when observed ozone exceeds the NAAQS threshold. These stratospheric intrusions elevated background ozone concentrations (estimated by turning off North American anthropogenic emissions in the model) to MDA8 values of 60–75 ppbv. At high-elevation western U.S. sites, the 25th–75th percentile of the stratospheric contribution is 15–25 ppbv when observed MDA8 ozone is 60–70 ppbv, and increases to ∼17–40 ppbv for the 70–85 ppbv range. These estimates, up to 2–3 times greater than previously reported, indicate a major role for stratospheric intrusions in contributing to springtime high-O3events over the high-altitude western U.S., posing a challenge for staying below the ozone NAAQS threshold, particularly if a value in the 60–70 ppbv range were to be adopted.