documentclass[a4paper,twoside,openright,11pt]{report}

usepackage{fancyhdr}
pagestyle{fancy}
fancyhf{}
fancypagestyle{MyStyle}{
fancyhead[RO]{nouppercase{rightmark}}
fancyhead[LE]{leftmark}
fancyfoot[C]{thepage}
}
usepackage{blindtext}

begin{document}
pagestyle{MyStyle}
chapter{First chapter}
blindtext[5]
end{document}