It's a tricky one, isn't it? I think it comes down to a cost / benefit thing. If you pay once, he'll expect it every year, so that becomes a structural cost of employing him, and potentially anyone else he tells. There is also the "emotional cost" of your irked status, which is hard to put a montary value on.
On the plus side, if you do pay, you may be securing a happy, productive worker. If the quality of his work is good enough, it might be worth taking the financial hit, swallowing the irked feelings, and thinking of it as a cost of business.
A lot also depends on your sense of the motivation here. If he's a good, hard worker asking for a reward for a job well done, I'd be inclined to reward him. If he's just trying to see if he can get the stupid Westener to cough up a bit of cash for Christmas, cut your losses and dump him. In that case, it's clear that he sees your relationship in terms of what he can get from you, rather than what value he can provide for you, and it's likely an early signal of impending shoddiness. Since he has asked, it's clear he thinks he is entitled to a bonus. If you disappoint that sense of entitilement (deserved or not), you've got a disgruntled employee
<added>
>> It smacks of:
>> "What else can I get out of this Guy, he seems a soft touch"
Yeah, might be inclined to get rid then. Sounds like it's the tip of an iceberg, change course whilst ye may