Test if the first character of a string is 'a'

The xstring package offers plenty of useful commands for string manipulation. However, if you're worried about performance for a very specific task, you may want to use lower-level commands, as in egreg's and Qrrbrbirlbel's answers.

Here's a solution using xstring; note that the argument to \testchain is fully expanded, if any expansion can be applied.

\documentclass{article}

\usepackage{xstring}

\newcommand\testchain[1]{%
  \StrLeft{#1}{1}[\firstchar]%
  \IfStrEq{\firstchar}{a}{true}{false}%
}

\begin{document}

\noindent
    Test 1: \testchain{adfgi7634r}\\
    Test 2: \testchain{sdfkhsdf}\\  
    \def\abc{abc}
    \def\ghi{ghi}
    Test 3: \testchain{\abc}\\
    Test 4: \testchain{\ghi}
\end{document}

This is an expandable test, which means it can be used in an \edef as shown in the last line:

\documentclass{article}
\usepackage{xparse}

\makeatletter
\newcommand\testchain[1]{%
  \ifnum\pdfstrcmp{\unexpanded\expandafter{\@car#1\@nil}}{a}=\z@
    \expandafter\@firstofone
  \else
    \expandafter\@gobble
  \fi{true}%
}
\def\testchain@a{a}
\makeatother

\begin{document}
X\testchain{a}X

X\testchain{abc}X

X\testchain{x}X

\edef\exptest{\testchain{abc}}\texttt{\meaning\exptest}
\end{document}

It uses \pdfstrcmp and \unexpanded, so it's not available in "classic TeX". If you plan to use the macro with XeLaTeX or LuaLaTeX, then load the package pdftexcmds and use \@pdfstrcmp instead of \pdfstrcmp.

---

Here is a LaTeX3 version.

\documentclass{article}
\usepackage{xparse}
\ExplSyntaxOn
\DeclareExpandableDocumentCommand{\testchain}{m}
 {
  \testchain_main:n { #1 }
 }
\cs_new:Npn \testchain_main:n #1
 {
  \str_if_eq_x:nnT { \tl_head:n { #1 } } { a } { true }
 }
\ExplSyntaxOff

\begin{document}
X\testchain{a}X

X\testchain{abc}X

X\testchain{x}X

\edef\exptest{\testchain{abc}}\texttt{\meaning\exptest}
\end{document}

A variant that allows to use a string buried into a macro, by calling \testchain*:

\documentclass{article}
\usepackage{xparse}
\ExplSyntaxOn
\DeclareExpandableDocumentCommand{\testchain}{sm}
 {
  \IfBooleanTF{#1}
   { \testchain_main:o { #2 } }
   { \testchain_main:n { #2 } }
 }
\cs_new:Npn \testchain_main:n #1
 {
  \str_if_eq_x:nnT { \tl_head:n { #1 } } { a } { true }
 }
\cs_generate_variant:Nn \testchain_main:n { o }
\ExplSyntaxOff

\begin{document}
X\testchain{a}X

X\testchain{abc}X

X\testchain{x}X

\def\stringI{abc}
X\testchain{\stringI}X

% show it's fully expandable
\edef\exptest{\testchain*{\stringI}}\texttt{\meaning\exptest}
\end{document}

I present a Lua solution which works with all macro packages, including plainTeX, ConTeXt and LaTex. It defines a simple Lua funktion testing for the first character. Then a TeX macro is defined calling the Lua funktion.

\def\beginsWith#1#2#3%
  {\directlua{userdata.beginsWith([===[#1]===],[===[#2]===],[===[#3]===])}}

\directlua{
  userdata = userdata or {}
  userdata.beginsWith = function(str, arg2, arg3)
    if string.find(str, "^a") then
      tex.print(arg2)
    else
      tex.print(arg3)
    end
  end}

\beginsWith{abcde}{true}{false}\par
\beginsWith{zyxwv}{true}{false}
\bye

The output:

true
false