In the report class, it's the \chapter command that selects the page style for the first chapter page:
\newcommand\chapter{\if@openright\cleardoublepage\else\clearpage\fi
\thispagestyle{plain}%
\global\@topnum\z@
\@afterindentfalse
\secdef\@chapter\@schapter}
Thus a solution is to change plain into empty, by adding the following to the document preamble:
\makeatletter
\renewcommand\chapter{\if@openright\cleardoublepage\else\clearpage\fi
\thispagestyle{empty}%
\global\@topnum\z@
\@afterindentfalse
\secdef\@chapter\@schapter}
\makeatother
If you don't plan to use the plain pagestyle, then a simpler
\makeatletter
\let\ps@plain\ps@empty
\makeatother
would suffice.
A similar patch should probably be made also to \part; you can get both with this alternative code that doesn't require looking at report.cls in order to find the definitions:
\usepackage{etoolbox}
\patchcmd{\chapter}{plain}{empty}{}{}
\patchcmd{\part}{plain}{empty}{}{}
\thispagestyle{empty}just after\chapter{...}. – guillem Mar 21 '13 at 07:27