Understanding the conformational statistics of a semiflexible polymer confined to a channel is a fundamental problem in polymer physics. This problem has attracted a lot of attention in recent years, owing to the fact that
recent experiments on DNA molecules confined in nanochannels are well described by this model. Simulations and mean-field estimates have shown that semiflexible polymers exhibit a number of scaling regimes, depending on the strength of confinement. In the so-called extended de Gennes regime, we show that it is possible to exactly map the statistics of the polymer to a one-dimensional model known as the weakly self-avoiding random walk. Applying results derived for the 1D model yields exact predictions for the confined polymer, which we have confirmed by computer simulations and experimental measurements on DNA.