The observed number counts of high-redshift galaxy candidates have been used to build up a statistical description of star-forming activity at redshift z ≳ 7, when galaxies reionized the Universe. Standard models predict that a high incidence of gravitational lensing will probably distort measurements of flux and number of these earliest galaxies. The raw probability of this happening has been estimated to be ∼0.5 per cent (refs 11, 12), but can be larger owing to observational biases. Here we report that gravitational lensing is likely to dominate the observed properties of galaxies with redshifts of z ≳ 12, when the instrumental limiting magnitude is expected to be brighter than the characteristic magnitude of the galaxy sample. The number counts could be modified by an order of magnitude, with most galaxies being part of multiply imaged systems, located less than 1 arcsec from brighter foreground galaxies at z ≈ 2. This lens-induced association of high-redshift and foreground galaxies has perhaps already been observed among a sample of galaxy candidates identified at z ≈ 10.6. Future surveys will need to be designed to account for a significant gravitational lensing bias in high-redshift galaxy samples.