New results are presented, as part of the Hi-z Emission Line Survey (HiZELS), from the largest area survey to date (1.4 sq.deg) for Lyman-alpha emitters (LAEs) at z~9. The survey, which is primarily targeting H-alpha emitters at z<3, uses the Wide Field CAMera on the United Kingdom Infrared Telescope and a custom narrow-band filter in the J band and reaches a Lyman-alpha luminosity limit of ~10^43.8 erg/s over a co-moving volume of 1.12x10^6 Mpc^3 at z=8.96+-0.06. Only 2 candidates were found out of 1517 line emitters and those were rejected as LAEs after follow-up observations. The limit on the space density of bright LAEs is improved by 3 orders of magnitude, consistent with suppression of the bright end of the Lyman-alpha luminosity function beyond z~6. Combined with upper limits from smaller but deeper surveys, this rules out some of the most extreme models for high-redshift LAEs. The potential contamination of future narrow-band Lyman-alpha surveys at z>7 by Galactic brown dwarf stars is also examined, leading to the conclusion that such contamination may well be significant for searches at 7.7<z<8.0, 9.1<z<9.5 and 11.7 < z < 12.2.