Can a truly randomized procedure (e.g. random treatment allocation) result in unbalanced distributions? Thousands of randomized trials are ongoing or in the planning. These trials rely on randomization procedures (e.g. patients being randomized to either placebo or active drugs) to yield two balanced groups, who do not differ significantly for any imaginable variable.
But what are the chances that such a randomization yields unbalanced groups? 
Is there a chance that randomness is not random?
What could the causes be? Is it a technical/software issue or is it mere probability?
 A: As for the chances, that is difficult to assess. But one always should run tests on the baseline and attest if the variables that might be related to the treatment hold any difference between treatment and control groups. If you need some correction, you might run a propensity score on your sample in order to match your sample adequately. 
Below I will list some of the possibilities of the biases that you might run on randomized experiments.
By Heckman and Smith (1995), in experiments that are also randomized by locality, you might have groups of people who will anticipate the program and move to the region of treatment -- this is a bias that might be hard to overcome, I believe, if that is a possibility. 
Also, control groups might change their behavior. Say, when there is a conditionality of schooling frequency to receive the treatment. If the control group knows it will receive the treatment benefit in the near future, the group might behave similarly to the treatment group in order to the receive the treatment in the near future. Another bias might be related to other social programs that one of the groups or both the control and the treatment group might be receiving. 
One more bias that is frequently studied today it is related to spillover effects from the treated to the control groups (the violation of the SUTVA hypothesis). If we are considering a money benefit inside a village in which both control and treatment groups engage, one should consider general equilibrium effects -- for instance, money lending by extended families (thus money going from treatment to control groups), an idea tested by Angelucci and Giorgi (2009).
Edit: As for the 'truly randomized procedure' you mean what exactly?  
