We report a case of a 65-year-old male patient who presented with gradually worsening dyspnea over 2 years. History was significant for smoking and the absence of any hazardous occupational exposure. The clinical findings at presentation included absent breath sounds and stony dullness on the left side, with tracheal deviation contralaterally and clubbing. A chest roentgenogram showed a left-sided opacity occupying almost the entire left hemithorax. A subsequent CT scan of the chest revealed an intrathoracic, extrapulmonary lesion producing a mediastinal shift. Surgical resection of the mass was performed, and pathology, along with immunohistochemical studies positive for CD34 and negative for epithelial markers, confirmed the diagnosis of solitary fibrous tumor of the pleura (SFTP). SFTP is a rare neoplasm, and diagnosis is often difficult. Suspicion of SFTP should arise in the setting of a patient presenting with a paucity of symptoms (except in the case of an accompanying paraneoplastic syndrome), the absence of exposure to asbestos, and a large mass with sharp margins and encapsulation seen on a chest radiograph.