We introduce a novel feature descriptor to describe cancer cells called Cell Orientation Entropy (COrE). The main objective of this work is to employ COrE to quantitatively model disorder of cell/nuclear orientation within local neighborhoods and evaluate whether these measurements of directional disorder are correlated with biochemical recurrence (BCR) in prostate cancer (CaP) patients. COrE has a number of novel attributes that are unique to digital pathology image analysis. Firstly, it is the first rigorous attempt to quantitatively model cell/nuclear orientation. Secondly, it provides for modeling of local cell networks via construction of subgraphs. Thirdly, it allows for quantifying the disorder in local cell orientation via second order statistical features. We evaluated the ability of 39 COrE features to capture the characteristics of cell orientation in CaP tissue microarray (TMA) images in order to predict 10 year BCR in men with CaP following radical prostatectomy. Randomized 3-fold cross-validation via a random forest classifier evaluated on a combination of COrE and other nuclear features achieved an accuracy of 82.7 ± 3.1% on a dataset of 19 BCR and 20 non-recurrence patients. Our results suggest that COrE features could be extended to characterize disease states in other histological cancer images in addition to prostate cancer.