We present PolyChor$λ$, a language for higher-order functional \emph{choreographic programming} -- an emerging paradigm by which programmers write the desired cooperative behaviour of a system of communicating processes and then compile it into distributed implementations for each process, a translation called \emph{endpoint projection}. Unlike its predecessor, Chor$λ$, PolyChor$λ$ has both type and \emph{process} polymorphism inspired by System F$_ω$. That is, PolyChor$λ$ is the first (higher-order) functional choreographic language which gives programmers the ability to write generic choreographies and determine the participants at runtime. This novel combination of features also allows PolyChor$λ$ processes to communicate \emph{distributed values}, leading to a new and intuitive way to write delegation. While some of the functional features of PolyChor$λ$ give it a weaker correspondence between the semantics of choreographies and their endpoint-projected concurrent systems than some other choreographic languages, we still get the hallmark end result of choreographic programming: projected programs are deadlock-free by design.