Soils, sediments, freshwaters, and marine waters contain natural organic matter (NOM), an exceedingly complex mixture of organic compounds that collectively exhibit a nearly continuous range of properties (size-reactivity continuum). NOM is composed mainly of carbon, hydrogen, and oxygen, with minor contributions from heteroatoms such as nitrogen, sulfur, and phosphorus. Suwannee River fulvic acid (SuwFA) is a fraction of NOM that is relatively depleted in heteroatoms. Ultrahigh resolution Fourier transform ion cyclotron (FTICR) mass spectra of SuwFA reveal several thousand molecular formulas, corresponding in turn to several hundred thousand distinct chemical environments of carbon even without accountancy of isomers. The mass difference deltam among adjoining C,H,O-molecules between and within clusters of nominal mass is inversely related to molecular dissimilarity: any decrease of deltam imposes an ever growing mandatory difference in molecular composition. Molecular formulas that are expected for likely biochemical precursor molecules are notably absent from these spectra, indicating that SuwFA is the product of diagenetic reactions that have altered the major components of biomass beyond the point of recognition. The degree of complexity of SuwFA can be brought into sharp focus through comparison with the theoretical limits of chemical complexity, as constrained and quantized by the fundamentals of chemical binding. The theoretical C,H,O-compositional space denotes the isomer-filtered complement of the entire, very vast space of molecular structures composed solely of carbon, hydrogen, and oxygen. The molecular formulas within SuwFA occupy a sizable proportion of the theoretical C,H,O-compositional space. A 100 percent coverage of the theoretically feasible C,H,O-compositional space by SuwFA molecules is attained throughout a sizable range of mass and H/C and O/C elemental ratios. The substantial differences between (and complementarity of) the SuwFA molecular formulas that are observed using six different modes of ionization (APCI, APPI, and ESI in positive and negative modus) imply considerable selectivity of the ionization process and suggest that the observed mass spectra represent simplified projections of still more complex mixtures.