Idiopathic pulmonary fibrosis (IPF) is an illness characterized by progressive decline in lung function and premature death from respiratory failure. Fibrocytes are a novel population of bone marrow-derived circulating progenitor cells that have been shown to traffic to the lungs and contribute to fibrosis in animal models of pulmonary fibrosis, and whose numbers correlate with the degree of fibrosis and with survival in human pulmonary fibrosis. The investigators propose to test the hypothesis that therapy with the mTOR inhibitor, sirolimus, reduces the number of circulating fibrocytes in patients with IPF. The investigators propose to test this hypothesis in short-term pilot trial of sirolimus in patients with IPF to determine its effect on the number and phenotype of circulating fibrocytes.