1. Department of Physics, Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08544, USA
   
2. Central Research Institute of Electric Power Industry, Komae, Tokyo 201-8511, Japan
   
3. These authors contributed equally to this work.

Correspondence to: Ali Yazdani¹ Correspondence and requests for materials should be addressed to A.Y. (Email: yazdani@princeton.edu).

Pairing of electrons in conventional superconductors occurs at the superconducting transition temperature T_c, creating an energy gap in the electronic density of states (DOS)¹. In the high-T_c superconductors, a partial gap in the DOS exists for a range of temperatures above T_c (ref. 2). A key question is whether the gap in the DOS above T_c is associated with pairing, and what determines the temperature at which incoherent pairs form. Here we report the first spatially resolved measurements of gap formation in a high-T_c superconductor, measured on Bi₂Sr₂CaCu₂O₈₊ samples with different T_c values (hole concentration of 0.12 to 0.22) using scanning tunnelling microscopy. Over a wide range of doping from 0.16 to 0.22 we find that pairing gaps nucleate in nanoscale regions above T_c. These regions proliferate as the temperature is lowered, resulting in a spatial distribution of gap sizes in the superconducting state^{3, 4, 5}. Despite the inhomogeneity, we find that every pairing gap develops locally at a temperature T_p, following the relation 2/k_BT_p = 7.9  0.5. At very low doping (0.14), systematic changes in the DOS indicate the presence of another phenomenon^{6, 7, 8, 9}, which is unrelated and perhaps competes with electron pairing. Our observation of nanometre-sized pairing regions provides the missing microscopic basis for understanding recent reports^{10, 11, 12, 13} of fluctuating superconducting response above T_c in hole-doped high-T_c copper oxide superconductors.