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The last decade has seen a sharp increase in Internet traffic due to dispersion of videos. Despite this growth, user's quality of experience (QoE) in peer-to-peer (P2P) streaming systems does not match the conventional television service. The deployment of P2P streaming system is affected by long delay, unplanned interruption, flash crowd, high churn situation and choice of overlay structure. The overlay structure plays significant role in ensuring that traffic are distributed to all physical links in a dynamic and fair manner, tree-based (TB) and mesh-based (MB) are the most popular. TB fails in situations where there is failure at the parent peer which can lead to total collapse of the system while MB is more vulnerable to flash crowd and high churn situation due to its unstructured pattern. This paper presents a novel P2P streaming topology (UStream), using a hybrid of TB and MB to address the disadvantages of both topologies to ensure an optimal solution. Furthermore, UStream adopts the features of ultra-metric tree to ensure that the time taken from the root peer to any of the children's peer are equal and the spanning tree to monitor all the peers at any point in time. Ustream also employs the principle of chaos theory. The present peer determines the future, though the approximate present does not approximately determines the future. Ustream was formalized using mathematical theories. Several theorems were proposed and proved in validating this topology.