  Carbon, nitrogen, and oxygen are the fourth, sixth, and third most abundant
elements in the Sun. Their abundances remain hotly debated due to the so-called
solar modelling problem that has persisted for almost $20$ years. We revisit
this issue by presenting a homogeneous analysis of $408$ molecular lines across
$12$ diagnostic groups, observed in the solar intensity spectrum. Using a
realistic 3D radiative-hydrodynamic model solar photosphere and LTE (local
thermodynamic equilibrium) line formation, we find $\log\epsilon_{C} =
8.47\pm0.02$, $\log\epsilon_{N} = 7.89\pm0.04$, and $\log\epsilon_{O} =
8.70\pm0.04$. The stipulated uncertainties mainly reflect the sensitivity of
the results to the model atmosphere; this sensitivity is correlated between the
different diagnostic groups, which all agree with the mean result to within
$0.03$ dex. For carbon and oxygen, the molecular results are in excellent
agreement with our 3D non-LTE analyses of atomic lines. For nitrogen, however,
the molecular indicators give a $0.12$ dex larger abundance than the atomic
indicators, and our best estimate of the solar nitrogen abundance is given by
the mean: $7.83$ dex. The solar oxygen abundance advocated here is close to our
earlier determination of $8.69$ dex, and so the present results do not
significantly alleviate the solar modelling problem.
