The simultaneous production of two J/psi mesons has been significantly observed in proton-proton collisions at a center-of-mass energy of 7 TeV with the CMS detector. The two J/psi mesons are fully reconstructed in their decay to muons. The signal yield is extracted with an extended maximum likelihood fit based on four event variables. A method was developed to correct for detector acceptances and efficiencies based on the measured momenta of the J/psi and their decay muons to maintain the least model dependence possible. The measurement is performed in an acceptance region defined by the individual J/psi transverse momentum and rapidity. From the measured signal yield of 446 events corresponding to an integrated luminosity of 4:7 inverse femtobarn. The total cross section is found to be 1:49 nanobarn, with 0:07 statistical and 0:13 nb systematic error, and unpolarizaed production was assumed. Most predictions for particle production at the LHC assume dominance of single parton interaction for proton-proton collisions, which can be tested with the final state measured in this analysis. The differential cross section is measured in bins of the double J/psi invariant mass, the double J/psi transverse momentum, and the absolute difference in rapidity of the two J/psi. The reconstruction of the four charged muon trajectories heavily relies on the Pixel subdetector located close to the beampipe. Systematic studies with cosmic muons and tracks from collision events are presented. The development of the Pixel RawToDigi package, data quality monitoring packages, commissioning studies of Pixel data and tracks in first collisions, and realistic simulations of decay signals in the pixel subdetector were all performed as a part of this dissertation work.