  The reaction $\gamma p \to pK^+K^-$ was studied at Jefferson Lab with photon
energies from 1.8 to 3.8 GeV using a tagged photon beam. The goal was to search
for a $\Theta^{++}$ pentaquark, a narrow doubly charged baryon state having
strangeness S=+1 and isospin I=1, in the $pK^+$ invariant mass spectrum. No
statistically significant evidence of a $\Theta^{++}$ was found. Upper limits
on the total and differential production cross section for the reaction $\gamma
p \to K^-\Theta^{++}$ were obtained in the mass range from 1.5 to 2.0
GeV/c$^2$, with an upper limit of about 0.15 nb, 95% C.L. for a narrow
resonance with a mass $M_{\Theta^{++}}=1.54$ GeV/c$^2$. This result places a
very stringent upper limit on the $\Theta^{++}$ width.
