Um, he's mad at YOU because he's worried HIS dog will eat YOUR chickens? That's some pretty !@#$ed up logic. He shouldn't be letting his dog off the leash, particularly when there are leash laws.
That being said, being combative is rarely helpful, and threatening to call the authorities on him is likely to just create more hostility, and you do have to live near this guy. What if you approached him with some eggs as a gift, and start by illustrating all you have in common: you're both animal lovers (presumably), or at least animal owners, both of you want everyone's animals in the neighborhood to be safe, and both of you want to respect your neighbors' rights to care for their animals in the way that seems best to them. Try to get him to agree with you from the outset so he's in a more friendly, receptive frame of mind.
Then tell him how much you appreciate his keeping his dog safely confined, which is evident from the fact that he's never attacked any of your chickens (assuming that's true?), and that you feel confident that he's a responsible pet-owner who respects the laws and the best interests of the neighborhood. Perhaps your confidence in his good behavior will inspire him to be more considerate and realize where the responsibility for his dog's actions really lies. Once he sees that you're trying to be friendly and neighborly, that you're generous enough to share the bounty of your flock, and that you see him as a like-minded ally and not an enemy, he may well change his attitude.
Even if you're worried the relationship is already too embittered to be improved, an act of outreach and a show of sympathetic understanding, even if it's a little forced, can go a long way towards changing people's minds. As Dale Carnegie says, you can never win an argument, even when you're right, because when people feel attacked, they dig in and become defensive. Most people are too proud to let their minds be changed simply by being shown the facts of why they're wrong. Much better to disarm them with kindness and win them over with overtures of friendship, or at least empathy. Then they'll often come to the correct conclusion on their own.