I have been eating the whole plants for this summer so far, not gotten any bad effects, trying to find things such as stinging nettles, Chia plants seem to have a ton of protein and antioxidants.
I can't imagine that they are toxic if eaten not in excess.
For example, the flowers from the locusts trees are totally eligible, yet if you have never ate them before and eat a bunch, you will get sick to your stomach, it's not because of a toxin, but just that most of our bodies have not encountered such food,and at 1st will respond to it as a poison.
At any rate I have never gotten ill from raw or cooked greens , even Chia plants, though I eat dandelion, burdock and other wild edibles, so I might not be the average person to speak about this.
Do your own research, eat small amounts at first to see how well you tolerate them, though I don't think anyone is going to be hurt by eating Chia greens
I am open to any other ideas or experiences with this plant, as it's so easy to grow, has half the protein of Stinging Nettles, and is almost impossible to get rid of, much like minting that respect.