We describe the histogram of chain conformations that results when flexible polymers adsorb more quickly than the surface structure equilibrates. By infrared analysis of conformational substates in a model system (poly(methyl methacrylate) adsorbed primarily by hydrogen bonding onto oxidized silicon), this histogram was measured and found to be bimodal. One large population of chains spread into flattened conformations. A second large population of chains, finding less free surface available at the time of adsorption, became attached more tenuously. The history dependence of adsorption could be understood as the irreversible adsorption of objects with flexible shape. This interpretation differs decisively from the traditional considerations of minimizing the free energy.