Alzheimer's disease is characterized by the misfolding and self-assembly of the amyloidogenic protein amyloid-β (Aβ). The aggregation of Aβ leads to diverse oligomeric states, each of which may be potential targets for intervention. Obtaining insight into Aβ oligomers at the atomic level has been a major challenge to most techniques. Here, we use magic angle spinning recoupling 1H-1H NMR experiments to overcome many of these limitations. Using 1H-1H dipolar couplings as a NMR spectral filter to remove both high and low molecular weight species, we provide atomic-level characterization of a non-fibrillar aggregation product of the Aβ1-40 peptide using non-frozen samples without isotopic labeling. Importantly, this spectral filter allows the detection of the specific oligomer signal without a separate purification procedure. In comparison to other solid-state NMR techniques, the experiment is extraordinarily selective and sensitive. A resolved 2D spectra could be acquired of a small population of oligomers (6 micrograms, 7% of the total) amongst a much larger population of monomers and fibers (93% of the total). By coupling real-time 1H-1H NMR experiments with other biophysical measurements, we show that a stable, primarily disordered Aβ1-40 oligomer 5-15 nm in diameter can form and coexist in parallel with the well-known cross-β-sheet fibrils.