Largo can, in fact, seize the attack of chances. Nothing says that you can only take opportunity attacks when it is not your turn, and nothing says that you can not take an opportunity attack by doing something else. Opportunity attacks are not actions, so an action occurring in the middle of a full action as a charge is admissible.
It's impossible to prove a negative, but the rules on opportunity attacks simply do not mention anything like that.
The word "turn" is used only three times, and all this to explain how opportunity attacks interrupt a turn, and after it is resolved, this turn continues. The rules say that you can make an opportunity attack "even when it's not your action "(accentuation mine), but the word "same" here indicates that it is an inclusive, non-exhaustive statement – you can do it "same" when you might expect otherwise. This implies that not only you can when it is "your action", but that the author considers that it is the most anticipated case (and this would indeed be the case for other combat events).
The word "action" is used eleven times – once in the quote above on the attack "even when it's not your action", then ten times to describe various kinds of actions that provoke. Note the unusual wording "your action" to indicate your turn – this was common at the beginning of the 3.5rd and was avoided in subsequent books because it was confusing.
So anyway, the flow here would be that Largo starts charging, triggering the count's prepared action. This interrupts Largo's charge and begins the Count's charge. When the count begins to close less than 10 feet from Largo within 5 feet, it causes Largo. This interrupts the Count's charge, allowing Largo to attack by chance. Once Largo does this, the count's interrupted charge resumes and the count moves next to Largo and attacks with the corresponding bonuses. This being resolved, Largo's action resumes, allowing Largo to hit the account or continue charging to his original target (provided that the account is not embarrassing for the moment).
If we wanted to make this more ridiculous, we could have Largo take his second-hand attack with a bare-handed strike, but without an Improved Hand Strike, which would cause the count, who would get an exit attack before Largo can not finish it. The rest of the events would solve the same problems.