GRB 221009A is the brightest gamma-ray burst ever detected. To probe the very-high-energy (VHE, >100 GeV) emission, the High Energy Stereoscopic System (H.E.S.S.) began observations 51.8 hours after the triggering event, when the brightness of the moonlight no longer precluded observations. No significant VHE emission from the gamma-ray burst is detected in an analysis with H.E.S.S. data. Differential and integral upper limits are computed using data from the third, fourth, and ninth nights after the initial detection of the GRB. The constraints derived from the H.E.S.S. observations complement the available multi-wavelength data. For example, the afterglow of GRB 221009A presents a novel opportunity to explore extreme Klein-Nishina effects, for which upper limits in the VHE band are valuable. We will present and discuss the results of the analysis and highlight the important role of IACTs in following up such powerful events.