We combine a semi-analytical model of galaxy formation with a very large simulation which follows the growth of a large-scale structure in a Λ cold dark matter (ΛCDM) universe to predict the clustering of Lyα emitters. We find that the clustering strength of Lyα emitters has only a weak dependence on Lyα luminosity but a strong dependence on redshift. With increasing redshift, Lyα emitters trace progressively rarer, higher density regions of the universe. Due to the large volume of the simulation, over 100 times bigger than any previously used for this application, we can construct mock catalogues of Lyα emitters and study the sample variance of current and forthcoming surveys. We find that the number and clustering of Lyα emitters in our mock catalogues are in agreement with measurements from current surveys, but there is a considerable scatter in these quantities. We argue that a proposed survey of emitters at z= 8.8 should be extended significantly in solid angle to allow a robust measurement of Lyα emitter clustering.