We have studied the chemical composition of NGC 1806, a massive, intermediate-age globular cluster that shows a double main sequence turnoff. We analyzed a sample of high-resolution spectra (secured with FLAMES at the Very Large Telescope) for 8 giant stars, members of the cluster, finding an average iron content of [Fe/H]=--0.60 +- 0.01 dex and no evidence of intrinsic star-to-star variations in the abundances of light elements (Na, O, Mg, Al). Also, the (m_(F814W); m_(F336W)-m_(F814W)) color-magnitude diagram obtained by combining optical and near-UV Hubble Space Telescope photometry exhibits a narrow red giant branch, thus ruling out intrinsic variations of C and N abundances in the cluster. These findings demonstrate that NGC 1806 does not harbor chemically distinct sub-populations, at variance with what was found in old globular clusters. In turn, this indicates that the double main sequence turnoff phenomenon cannot be explained in the context of the self-enrichment processes usually invoked to explain the chemical anomalies observed in old globulars. Other solutions (i.e., stellar rotation, merging between clusters or collisions with giant molecular clouds) should be envisaged to explain this class of globulars.