Chroma is one of my favorite yarns to make things like small shawls, cowls and scarves. It's so soft and squishy and the colors with long repeats are gorgeous. The one drawback, as you've noticed, is that it's not as durable as a plied yarn. It is a loosely spun single which makes it fairly delicate. I've never had mine break, but I am a medium tension knitter.
What cast-on are you using? I ask, because I have found when knitting with Chroma that I usually have to work a knitted or cable cast-on, because long-tail tends to make it untwist on itself making it very fragile.