  We study the structured rainbow Ramsey theory at uncountable cardinals. When
compared to the usual rainbow Ramsey theory, the variation focuses on finding a
rainbow subset that not only is of a certain cardinality but also satisfies
certain structural constraints, such as being stationary or closed in its
supremum. In the process of dealing with cardinals greater than $\omega_1$, we
uncover some connections between versions of Chang's Conjectures and instances
of rainbow Ramsey partition relations, addressing a question raised in
\cite{zhang}.
