A new measurement of the inclusive production cross section for $pp\ensuremath{\rightarrow}t\overline{t}$ is performed at a center-of-mass energy of 7 TeV using data collected by the CMS experiment at the LHC. The analysis uses a data sample corresponding to an integrated luminosity of $36\text{ }\text{ }{\mathrm{pb}}^{\ensuremath{-}1}$, and is based on the final state with one isolated, high transverse momentum muon or electron, missing transverse energy, and hadronic jets. The $t\overline{t}$ content of the selected events is enhanced by requiring the presence of at least one jet consistent with $b$-quark hadronization. The measured cross section is $150\ifmmode\pm\else\textpm\fi{}9(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}17(\mathrm{syst})\ifmmode\pm\else\textpm\fi{}6(\mathrm{lumi})\text{ }\text{ }\mathrm{pb}$ and is in agreement with higher-order QCD calculations. The combination of this measurement with a previous CMS result based on dileptons gives $154\ifmmode\pm\else\textpm\fi{}17(\mathrm{stat}+\mathrm{syst})\ifmmode\pm\else\textpm\fi{}6(\mathrm{lumi})\text{ }\text{ }\mathrm{pb}$.