This study present SocialStories - a system based on incremental clustering for streaming tweets, for identifying fine-grained stories within a broader trending topic on Twitter. The contributions include a novel tf-metric, called the inverse cluster frequency, and a decay weighting for entities. We present our experiments on 0.19 million tweets posted in June 2014, revolving around the mentions of a software brand before, during and after a marketing conference and a software release. The novelty of our work is the text-based similarity calculation metrics, including a new similarity metric, called the inverse cluster frequency, and time-specific metrics that allow for the decay of old entities with the passage of time and preserve the homogeneity and the freshness of stories. We report improved performance and higher recall of 80%, against the gold standard (posthoc journalistic reports), as compared to LDA-, and Wavelet-based systems. Our algorithm is able to cluster 80% of all tweets into story-based clusters, which are 86% pure. It also enables earlier detection of trending stories than manual reports, and is far more accurate in identifying fine-grained stories within sub-topics as compared to baseline systems.