We investigated the biological activity of a series of substituted chromeno[3,2-c]pyridines, including compounds previously synthesized by our group and novel compounds whose syntheses are reported here. Tandem transformation of their tetrahydropyridine ring under the action of activated alkynes yielding 2-vinylsubstituted chromones was used to prepare nitrogen-containing derivatives of a biologically active chromone system. The inhibitory activity of these chromone derivatives against acetylcholinesterase (AChE), butyrylcholinesterase (BChE) and carboxylesterase (CaE) was investigated using the methods of enzyme kinetics and molecular docking. Antioxidant (antiradical) activity of the compounds was assessed in the ABTS assay. The results demonstrated that a subset of the studied chromone derivatives selectively inhibit BChE but do not exhibit antiradical activity. In addition, the results of molecular docking effectively explained the observed features in the efficacy, selectivity, and mechanism of BChE inhibition by the chromone derivatives.