Hi-C is one of the main methods for investigating spatial co-localisation of DNA in the nucleus. However, the raw sequencing data obtained from Hi-C experiments suffer from large biases and spurious contacts, making it difficult to identify true interactions. Existing methods use complex models to account for biases and do not provide a significance threshold for detecting interactions. Here we introduce a simple binomial probabilistic model that resolves complex biases and distinguishes between true and false interactions. The model corrects biases of known and unknown origin and yields a p-value for each interaction, providing a reliable threshold based on significance. We demonstrate this experimentally by testing the method against a random ligation dataset. Our method outperforms previous methods and provides a statistical framework for further data analysis, such as comparisons of Hi-C interactions between different conditions. GOTHiC is available as a BioConductor package (http://www.bioconductor.org/packages/release/bioc/html/GOTHiC.html).