Do spikes in Twitter chatter about a firm precede unusual stock market trading activity for that firm? If so, Twitter activity may provide useful information about impending financial market activity in real-time. We study the real-time relationship between chatter on Twitter and the stock trading volume of 96 firms listed on the Nasdaq 100, during 193 days of trading in the period from May 21, 2012 to September 18, 2013. We identify observations featuring firm-specific spikes in Twitter activity, and randomly assign each observation to a ten-minute increment matching on the firm and a number of repeating time indicators. We examine the extent that unusual levels of chatter on Twitter about a firm portend an oncoming surge of trading of its stock within the hour, over and above what would normally be expected for the stock for that time of day and day of week. We also compare the findings from our explanatory model to the predictive power of Tweets. Although we find a compelling and potentially informative real-time relationship between Twitter activity and trading volume, our forecasting exercise highlights how difficult it can be to make use of this information for monetary gain.