We have discovered large amounts of molecular gas, as traced by CO emission, in the ram pressure stripped gas tail of the Coma cluster galaxy D100 (GMP 2910), out to large distances of about 50 kpc. D100 has a 60 kpc long, strikingly narrow tail, which is bright in X-rays and Halpha. Our observations with the IRAM 30 m telescope reveal in total &#732; {10}<SUP>9</SUP> {M}<SUB>&sun; </SUB> H<SUB>2</SUB> (assuming the standard CO-to-H<SUB>2</SUB> conversion) in several regions along the tail, thus indicating that molecular gas may dominate its mass. Along the tail, we measure a smooth gradient in the radial velocity of the CO emission that is offset to lower values from the more diffuse Halpha gas velocities. Such a dynamic separation of phases may be due to their differential acceleration by ram pressure. D100 is likely being stripped at a high orbital velocity &#8819; 2200 km s<SUP>-1</SUP> by (nearly) peak ram pressure. Combined effects of intra-cluster medium (ICM) viscosity and magnetic fields may be important for the evolution of the stripped interstellar matter. We propose that D100 has reached a continuous mode of stripping of dense gas remaining in its nuclear region. D100 is the second known case of an abundant molecular stripped gas tail, suggesting that conditions in the ICM at the centers of galaxy clusters may be favorable for molecularization. From comparison with other galaxies, we find that there is a good correlation between the CO flux and the Halpha surface brightness in ram pressure stripped gas tails, over &#732;2 dex.