My Kitty throws up sometimes!?

My Kitty throws up sometimes. It can happen any time of the day. This morning, (he sleeps with me, by my feet), he jumped down as soon as I got up, and threw up on our living room rug. While cleaning, I noticed that the food was almost undigested, some pieces even looked not chewed at all. This isn't the first time he did it. He does it several times a month, sometimes. He is a type of a cat that can eat a feather from a pillow or a thread (if he finds it loose), and he likes to eat fast with appetite. We had him since he was a kitten. I always try my best to hide any stringy items, that he can chew on or swallow, knowing his character. We give him a hairball remedy (like a paste) from time to time, but he still throws up sometimes. He's a big black cat - 18lb, not fat, he's just big. We buy him a Good Life cat food, which has no artificial colors or preservatives, and he likes it. What could be the reason for his throwing ups? Usually, if he eats and then starts running (he likes crazy chases with our other cat, sometimes) - then we know, it's because he upsets his stomach. But, like this morning, he was laying before he got nausea, so it can't be from running or chasing. Does anyone have an idea what is it? He'll be visiting his vet this summer, but I'd still want to know, if anyone had a similar problem, or knows what can it be? I'd be very thankful!!