What do you lot think I should do (it's short)?

There is this guy who acts overly chivalrous towards me but in a respectful way rather than a patronising way, and he is always staring and smiling at me. It's been a year and he hasn't done anything. We're both the same height even though he is a few years older than me; and we're from different ethnicities. In other words, I think he may have a fear of rejection, should I ask him out? I do like him, but I've never asked a guy out.