  A Kneser graph $KG_{n,k}$ is a graph whose vertices are in one-to-one
correspondence with $k$-element subsets of $[n],$ with two vertices connected
if and only if the corresponding sets do not intersect. A famous result due to
Lov\'asz states that the chromatic number of a Kneser graph $KG_{n,k}$ is equal
to $n-2k+2$. In this paper we study the chromatic number of a random subgraph
of a Kneser graph $KG_{n,k}$ as $n$ grows. A random subgraph $KG_{n,k}(p)$ is
obtained by including each edge of $KG_{n,k}$ with probability $p$. For a wide
range of parameters $k = k(n), p = p(n)$ we show that $\chi(KG_{n,k}(p))$ is
very close to $\chi(KG_{n,k}),$ a.a.s. differing by at most 4 in many cases.
Moreover, we obtain the same bounds on the chromatic numbers for the so-called
Schrijver graphs, which are known to be vertex-critical induced subgraphs of
Kneser graphs.
