Context. We previously detected 89.2 GHz J = 1−0 HCO⁺ absorption in 12 directions lacking detected CO emission in the outskirts of the Chamaeleon cloud complex and toward one sightline with integrated CO emission W_CO = 2.4 K km s⁻¹. Eight sightlines had a much larger mean column density of dark neutral medium (DNM) – gas not represented in HI or CO emission – and were found to have much higher mean molecular column density. The five other sightlines had little or no DNM and were found to have much smaller but still detectable N(HCO⁺). Aims. To determine the CO column density along previously observed Chamaeleon sightlines and to determine why CO emission was not detected in directions where molecular gas is present. Methods. We took ¹²CO J = 1−0 absorption profiles toward five sightlines having higher DNM and HCO⁺ column densities and one sightline with smaller N(DNM) and N(HCO⁺). We converted the integrated HCO⁺ optical depths to N(H₂) in the weak-excitation limit using N(HCO⁺)/N(H₂) = 3 × 10⁻⁹ and converted the integrated CO optical depths ϒ_CO to CO column density using the relationship N(CO) = 1.861 × 10¹⁵ cm⁻² ϒ_CO^1.131 found along comparable lines of sight that were previously studied in J = 1−0 and J = 2−1 CO absorption and emission. Results. CO absorption was detected along the five sightlines in the higher-DNM group, with CO column densities 4 × 10¹³ cm⁻²≲ N(CO) ≲10¹⁵ cm⁻² that are generally below the detectability limit of CO emission surveys. Conclusions. In the outskirts of the Chamaeleon complex, the presence of molecular DNM resulted primarily from small CO column densities at the onset of CO formation around the HI/H₂ transition in diffuse molecular gas. CO relative abundances N(CO)/H₂ ≲2 × 10⁻⁶ in the outskirts of Chamaeleon are comparable to those seen in UV absorption toward early-type stars, including in Chamaeleon.