I would get a trap. You just want to be sure, don't take any chances on your chicken's lives. It's not worth it. Even if you don't get one, your better safe than sorry. Plus you don't have to kill the fox if you don't want to assuming you catch one. Just keep it there for a while and when you...
Yeah, when two of my chickens were killed by a fox it was day as well. I was in our living room when I saw a fox outside. I thought it hadn't gotten them yet. I went outside and scared it away before it could get any more. I didn't even hear anything before looking outside.
I would be worried too. I had a chicken die of coccidiosis and I had no idea until people started talking about her weight. She was tiny! After a while we kept her in a secluded area with food, water, and a heat lamp. She wouldn't eat or drink by herself so we had to go in 3 times a day and...