Idea of 'parser' to make the writing of asynchronous functions chains easier
Interesting question,

I find this code hard to read, I wonder what you consider unreadable code.

Some remarks on 

pp_chain_function = function (fname,condition_string) {
var queue=this;
var prec_result = 'result_'+queue.queue_length;
queue.queue_string += !condition_string ? '.then(function(){return '+fname+'();})'
        :'.then(function('+prec_result+'){if('+prec_result+condition_string+'){return '+fname+'();}return $.when();})';
queue.length++;

return queue;
};



Use jsbeautifier.org, always
Prefixing with pp makes no good sense
Postfixing with _string makes little sense
prec_result &lt;- What does prec stand for
var queue=this;, you only need to re-assign this if you work with closures
Consider a templating function for your string building
That long ternary statements looks horrendous, consider splitting it over multiple lines


Some remarks on 

queue_object = {
    pp_chain : pp_chain_function,
    pp_fail : pp_fail_function
};  



You use queue_object as a prototype, consider changing the name to reflect, also, JavaScript ought to be written in lowerCamelCase: queue_object -> queueObject -> queuePrototype


Some remarks on

var chain = pp_begin(); //init the chain
    chain.pp_chain('async_0').pp_chain('async_1');  //add two standard async functions
    if(condition two){chain.pp_chain('async_2','.length&gt;0');} //if external conditions and async_1 gave a result with length&gt;0, execute async_2
    chain.pp_fail('fail_handler');  //add fail handler
    console.warn(chain);  //replace with eval if you want to actually run it



Indenting is messed up
You are putting conditions in strings.. 
I am fairly certain that either by making async_1 fail if length &lt; 1 or putting your check inside async_2 you could replace this with

$.when( async_0, async_1 )
  .then( async_2, fail_handler );



The biggest elephant in the room is of course eval, you loose proper stack-traces, debugging, tooling ( jshint, jsbeautifier ), and open yourself up to all kinds of pain. I would suggest that you post one of your unreadable scripts, perhaps we can show you how to use Q so that they become readable without resorting to .. this.