Occasionally spark plugs can be worn enough to cause the car to shake but that's unlikely. I would pull one and check the gap, make sure they aren't worn prematurely.
One of the motor mounts could already be broken on it, sadly that is something that plagues almost all of the older Hondas I've encountered, although for one so new it seems unlikely. It could be something being weak though- weak spark from worn plus, weak coil in one of the cylinders, weak spray from a clogged fuel injector- something like that.
It's not an all out misfire or the CEL would definitely be on. I can't remember if they started using MAF sensors on the air intake on Accords in 2003 or not. Do you know if your car has a MAF sensor?
THis would certainly be extreme, but a timing chain only develops enough slack to create bad ignition timing if the chain, guide/tensioner, or sprockets develop play. And the main condition that this happens under is oil starvation/neglect. Again, at that mileage it seems like such a slim chance.
If it were my car, I can tell you what I would do. I would replace the spark plugs, dump a bottle of fuel injector cleaner in it, and if that didn't fix it, I'd suck it up and get a $75 MAF sensor from a parts store.