The study of climate records in ice cores requires an accurate determination of annual layering within the cores in order to establish a depth-age relationship. Existing tools to delineate these annual layers are based on observations of changes in optical, chemical, and electromagnetic properties. In practice, no single technique captures every layer in all circumstances. Therefore, the best estimates of annual layering are produced by analyzing a combination of measurable ice properties. We present a novel and complimentary elastic wave remote sensing method based on laser ultrasonics. This method is used to measure variations in ultrasonic wave arrival times and velocity along the core with millimeter resolution. The laser ultrasound system does not require contact with the ice core and is non-destructive. Custom optical windows allow the source and receiver lasers to be located outside the cold room, while the core is scanned by moving it with a computer-controlled stage. We present results from Antarctic firn and ice cores that lack visual evidence of a layered structure, but do show travel-time and velocity variations. In the future, these new data may be used to infer stratigraphic layers from elastic parameter variations within an ice core, as well as analyze ice crystal fabrics.