They are scrub jays, not bluebirds. Bluebirds are smaller and I think they have red on them, we have them around as well. These guys are the size of a Robin
What a little S%@^! You could try to snipe it with a bb or pellet gun. Or set a pull string box trap. Wait for it to hop under the box and pull the string. You don't want this Jay to show its offspring this trick.
Well, today I set up our live trap (previously used to solve a racoon problem) with an egg in it. Left for town, back in about an hour, egg gone, trap not tripped
Now the trap has another egg in it and the trail camera is pointed at it so I can see how he does it. Maybe he is too light to trip the plate, we have accidently trapped birds before though............. Hoping I get him this time
He and probably his buddies are taking or ruining about 6 of my 15-20 eggs per day depending on how many trips I can take down to collect as the chicken coop is on the back 40 of the farm!