Context. More gas is inferred to be present in molecular cloud complexes than can be accounted for by H I and CO emission, a phenomenon known as dark neutral medium (DNM) or CO-dark gas for the molecular part. Aims. We aim to investigate whether molecular gas can be detected in Chamaeleon where gas column densities in the DNM were inferred and CO emission was not detected. Methods. We took λ3 mm absorption profiles of HCO⁺ and other molecules toward 13 background quasars across the Chamaeleon complex, only one of which had detectable CO emission. We derived the H₂ column density assuming N(HCO⁺)/N(H₂) = 3 × 10⁻⁹ as before. Results. With the possible exception of one weak continuum target, HCO⁺ absorption was detected in all directions, C₂H in eight directions and HCN in four directions. The sightlines divide into two groups according to their DNM content, with one group of eight directions having N(DNM) ≳ 2 × 10²⁰ cm⁻² and another group of five directions having N(DNM) < 0.5 × 10²⁰ cm⁻². The groups have comparable mean N(H I) associated with Chamaeleon 6−7 × 10²⁰ cm⁻² and total hydrogen column density per unit reddening 6−7 × 10²¹ cm⁻² mag⁻¹. They differ, however, in having quite different mean reddening 0.33 vs. 0.18 mag, mean N(DNM) 3.3 vs. 0.14 × 10²⁰ cm⁻² and mean molecular column density 2N(H₂) = 5.6 vs. 0.8 × 10²⁰ cm⁻². The gas at more positive velocities is enriched in molecules and DNM. Conclusions. Overall the quantity of H₂ inferred from HCO⁺ can fully account for the previously inferred DNM along the sightlines studied here. H₂ is concentrated in the high-DNM group, where the molecular fraction is 46% vs. 13% otherwise and 38% overall. Thus, neutral gas in the outskirts of the complex is mostly atomic but the DNM is mostly molecular. Saturation of the H I emission line profile may occur along three of the four sightlines having the largest DNM column densities, but there is no substantial reservoir of “dark” atomic or molecular gas that remains undetected as part of the inventory of dark neutral medium.