  The Hecke orbit conjecture asserts that every prime-to-$p$ Hecke orbit in a
Shimura variety is dense in the central leaf containing it. In this paper, we
prove the conjecture for certain irreducible components of Newton strata in
Shimura varieties of PEL type A and C, when $p$ is an unramified prime of good
reduction. Our approach generalizes Chai and Oort's method for Siegel modular
varieties.
