First measurements of dihadron correlations for charged particles are presented for central PbPb collisions at a nucleon-nucleon center-of-mass energy of 2.76 TeV over a broad range in relative pseudorapidity (Delta eta) and the full range of relative azimuthal angle (Delta phi). The data were collected with the CMS detector, at the LHC. A broadening of the away-side (Delta phi approximate to pi) azimuthal correlation is observed at all Delta eta, as compared to the measurements in pp collisions. Furthermore, long-range dihadron correlations in Delta eta are observed for particles with similar phi values. This phenomenon, also known as the "ridge", persists up to at least vertical bar Delta eta vertical bar = 4. For particles with transverse momenta (p(T)) of 2-4 GeV/c, the ridge is found to be most prominent when these particles are correlated with particles of p(T) = 2-6 GeV/c, and to be much reduced when paired with particles of p(T) = 10-12 GeV/c.