  We compute the free energy of confinement ${\cal{F}}$ for a wormlike chain
(WLC), with persistence length $l_p$, that is confined to the surface of a
cylinder of radius $R$ under an external tension $f$ using a mean field
variational approach. For long chains, we analytically determine the behavior
of the chain in a variety of regimes, which are demarcated by the interplay of
$l_p$, the Odijk deflection length ($l_d=(R^2l_p)^{1/3}$), and the Pincus
length ($l_f = {k_BT}/{f}$, with $k_BT$ being the thermal energy). The theory
accurately reproduces the Odijk scaling for strongly confined chains at $f=0$,
with ${\cal{F}}\sim Ll_p^{-1/3}R^{-2/3}$. For moderate values of $f$, the Odijk
scaling is discernible only when ${l_p}\gg R$ for strongly confined chains.
Confinement does not significantly alter the scaling of the mean extension for
sufficiently high tension. The theory is used to estimate unwrapping forces for
DNA from nucleosomes.
