A search is presented for standard model (SM) production of four top quarks t t ¯ t t ¯ (tt¯tt¯) in pp collisions in the lepton + jets channel. The data correspond to an integrated luminosity of 19.6 fb −1 recorded at a centre-of-mass energy of 8 TeV with the CMS detector at the CERN LHC. The expected cross section for SM t t ¯ t t ¯ tt¯tt¯ production is σ t t ¯ t t ¯ S M ≈ 1 f b σSMtt¯tt¯≈1fb . A combination of kinematic reconstruction and multivariate techniques is used to distinguish between the small signal and large background. The data are consistent with expectations of the SM, and an upper limit of 32 fb is set at a 95% confidence level on the cross section for producing four top quarks in the SM, where a limit of 32 ± 17 fb is expected.