The behavior of a grafted polymer chain confined in a tube is investigated within a scaling theory substantiated with biased Monte Carlo simulations of a self-avoiding walk (SAW) on a cubic lattice. All the statistical and thermodynamic properties of the chain follow from the knowledge of the joint distribution P(z,m) giving the probability to observe a length z and a number of contacts m, in a model where the energy of the chain in a given configuration is proportional to m. The analysis is based on the factorization of P(z,m) into the a priori distribution P(z) and the conditional probability P(m\z) of finding m contacts given that the chain length is z. P(m\z) is well-approximated by a Gaussian distribution. Taking the variance [m(2)]-(m) over bar (2) of this distribution into account, we obtain a nonmean-field expression for the free energy of the confined chain. We show that the coil-globule transition of the confined chain is independent of its size but depends on the pore diameter. Contrary to free, unconfined chains, it is always a continuous transition.