Is there such a thing as a chin implant? Will it make my face look longer?

Genioplasty. Genioplasty is a procedure in which your bone can be repositioned in any dimension. If your desire is to have a longer face, a genioplasty can give you the added vertical dimension you seek.
Yes and No. Chin implants are available and chin augmentation is a relatively common procedure. Chin implants are available in a variety of shapes and sizes but are generally not used to increase the height of the lower third of the face (and lengthen the face). Neck contouring (e.g. Liposuction) is often done with chin implant surgery - together improving chin neck angle & appearance of lower face & neck.