  At temperatures below 0.1 GK the $^{19}$F$(p,\gamma)^{20}$Ne reaction is the
only breakout path out of the CNO cycle. Experimental studies of this reaction
are challenging from a technical perspective due to copious $\gamma$-ray
background from the far stronger $^{19}$F$(p,\alpha)^{16}$O reaction channel.
Here we present the first inverse kinematics study of the
$^{19}$F$(p,\gamma)^{20}$Ne reaction, in which we measure the strength of the
323-keV resonance. We find a strength value of $\omega\gamma =
3.3^{+1.1}_{-0.9}$ meV, which is a factor of two larger than the most recent
previous study. The discrepancy is likely the result of a direct to ground
state transition which previous studies were not sensitive to. We also observe
the transition to the first $2^{-}$ state, which has not been observed for this
resonance in previous studies. A new thermonuclear reaction rate is calculated
and compared with the literature.
