Gun related violence is a complex issue and accounts for a large proportion of violent incidents. In the research reported in this paper, we set out to investigate the pro-gun and anti-gun sentiments expressed on a social media platform, namely Twitter, in response to the 2012 Sandy Hook Elementary School shooting in Connecticut, USA. Machine learning techniques are applied to classify a data corpus of over 700,000 tweets. The sentiments are captured using a public sentiment score that considers the volume of tweets as well as population. A web-based interactive tool is developed to visualise the sentiments and is available at http://www.gunsontwitter.com. The key findings from this research are: (i) There are elevated rates of both pro-gun and anti-gun sentiments on the day of the shooting. Surprisingly, the pro-gun sentiment remains high for a number of days following the event but the anti-gun sentiment quickly falls to pre-event levels. (ii) There is a different public response from each state, with the highest pro-gun sentiment not coming from those with highest gun ownership levels but rather from California, Texas and New York.