One way to do this would be to redefine the \chapter and \label commands such that the very first use \label following a \chapter sets the desired value.

At the invocation of a \label, the value of the parameter to \label is stored in \CurrentChapterLabel if the toggle isFirstLabel is set. This toggle is set to false upon the first invocation of \label, so that subsequent uses of \label will not overwrite the value of \CurrentChapterLabel.
At the beginning of each \chapter, the value of toggle isFirstLabel is set so that the next use of \label will be stored.
Notes:
I have used newtoggle from the etoolbox package as I prefer that syntax versus the \newif syntax. But if you don't want to include an additional package it should be pretty straightforward to adapt this to use \newif or some other conditional methods.
The options [openany] and \usepackage[paperwidth=11.0cm]{geometry} were only used to obtain a better image to illustrate the result.
The value defined in \DefaultChapterLabel is what is returned if an attempt to use \CurrentChapterLabel prior to using the \label macro within a \chapter:

Code:
\documentclass[openany]{book}
\usepackage[paperwidth=11.0cm]{geometry}
\usepackage{etoolbox}
\newtoggle{isFirstLabel}
\toggletrue{isFirstLabel}
\newcommand{\DefaultChapterLabel}{UNDEFINED}%
\newcommand{\CurrentChapterLabel}{\DefaultChapterLabel}%
\let\OldChapter\chapter
\let\OldLabel\label
\def\chapter{%
\renewcommand{\CurrentChapterLabel}{\DefaultChapterLabel}% reset
% Set so that the next usf \label will store its
% value in \CurrentChapterLabel
\global\toggletrue{isFirstLabel}%
\OldChapter% let \chapter do it's original job
}%
\renewcommand*{\label}[1]{%
\iftoggle{isFirstLabel}{%
% This is the first use of \label in this chapter
% so store its value, and reset the toggle so we don't
% store the next time \label is used.
\renewcommand{\CurrentChapterLabel}{#1}%
\global\togglefalse{isFirstLabel}%
}{}%
\OldLabel{#1}% let \label do it's original job
}%
\begin{document}
\chapter{Introduction} \label{intro}
\section{Intro Section One} \label{intro-section-one}
Current chapter label is: \CurrentChapterLabel
\chapter{Second Chapter} \label{second}
\section{Second Chapter Section One} \label{second-section-section-one}
Current chapter label is: \CurrentChapterLabel
% The following is to test what happens if we attempt to access
% the value of \CurrentChapterLabel prior to setting a \label
% within this chapter
\chapter{Third Chapter}
Current chapter label is: \CurrentChapterLabel
\end{document}
\newcommand*{\chaplabelname}{intro}\label{\chaplabelname}fit your needs? – Heiko Oberdiek Aug 04 '12 at 22:16