Since this is a key area that takes stress, this would not do! I took some fray Check and covered the offending area, carefully. This will cause the fabric to stiffen up and will result in plasticy-scratchy fibers. It may also create stains depending on your fabric, so apply with caution.
After letting the Fray Check dry, I began running a blanket stitch around the entire neckline. This added a subtle decorative edge, while also binding the offending frayed fibers back into place. I eyeballed the stitching length and width, but for perfect accuracy, measure everything first! I did this in white at Sven's request, but any color would work well and look good, to boot.