Chemotaxis is defined as the oriented movement of cells (or an organism) in response to a chemical gradient. Chemotaxis is defined as the oriented movement of cells (or an organism) in response to a chemical gradient. Many sorts of motile cells undergo chemotaxis. For example, bacteria and many amoeboid cells can move in the direction of a food source. In our bodies, immune cells like macrophages and neutrophils can move towards invading cells. Other cells, connected with the immune response and wound healing, are attracted to areas of inflammation by chemical signals. The simplest mathematical model in chemotaxis is given by the Keller-Segel model. In the derivation of a macroscopic model from basic physical principles, certain aspects of microscopic dynamics, e.g., fluctuations of molecules are disregarded; one can take into account these fluctuations by incorporating a stochastic process, which results in a stochastic partial differential equation. In the project, we will add a time-homogenous Wiener process to the Keller-Segel model and will investigate the impact of this noise term. In particular, we will show the existence of local solutions, global solutions or blow up, investigate the ergodic properties of the system and perform its numerical approximation.