Observation of Exclusive Charmonium Production and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>γ</mml:mi><mml:mi>γ</mml:mi><mml:mo>→</mml:mo><mml:msup><mml:mi>μ</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>μ</mml:mi><mml:mo>−</mml:mo></mml:msup></mml:math>in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi><mml:mover accent="true"><mml:mi>p</mml:mi><mml:mo>¯</mml:mo></mml:mover></mml:math>Collisions at<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msqrt><mml:mi>s</mml:mi></mml:msqrt><mml:mo>=</mml:mo><mml:mn>1.96</mml:mn><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mi>TeV</mml:mi></mml:math>

In CDF we have observed the reactions p + p[over] --> p + X + p[over], with X being a centrally produced J/psi, psi(2S), or chi_{c0}, and gammagamma-->micro;{+}micro;{-} in pp[over] collisions at sqrt[s] = 1.96 TeV. The event signature requires two oppositely charged central muons, and either no other particles or one additional photon detected. Exclusive vector meson production is as expected for elastic photoproduction, gamma + p --> J/psi(psi(2S)) + p, observed here for the first time in hadron-hadron collisions. We also observe exclusive chi_{c0} --> J/psi + gamma. The cross sections dsigma/dy|_{y = 0} for J/psi, psi(2S), and chi_{c0} are 3.92 +/- 0.25(stat) +/- 0.52(syst) nb, 0.53 +/- 0.09(stat) +/- 0.10(syst) nb, and 76 +/- 10(stat) +/- 10(syst) nb, respectively, and the continuum is consistent with QED. We put an upper limit on the cross section for Odderon exchange in exclusive J/psi production.