jats:titleAbstract</jats:title>jats:pWe consider a stochastic partial differential equation (SPDE) model for chemorepulsion, with non-linear sensitivity on the one-dimensional torus. By establishing an a priori estimate independent of the initial data, we show that there exists a pathwise unique, global solution to the SPDE. Furthermore, we show that the associated semi-group is Markov and possesses a unique invariant measure, supported on a Hölder–Besov space of positive regularity, which the solution law converges to exponentially fast. The a priori bound also allows us to establish tail estimates on the jats:inline-formulajats:alternativesjats:tex-math$$L^p$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:msup mml:miL</mml:mi> mml:mip</mml:mi> </mml:msup> </mml:math></jats:alternatives></jats:inline-formula> norm of the invariant measure which are heavier than Gaussian.</jats:p>