The real-time crash likelihood prediction model is an essential component of the proactive traffic safety management system. Over the years, numerous studies have attempted to construct a crash likelihood prediction model in order to enhance traffic safety, but mostly on freeways. In the majority of the existing studies, researchers have primarily employed a deep learning-based framework to identify crash potential. Lately, Transformer has emerged as a potential deep neural network that fundamentally operates through attention-based mechanisms. Transformer has several functional benefits over extant deep learning models such as Long Short-Term Memory (LSTM), Convolution Neural Network (CNN), etc. Firstly, Transformer can readily handle long-term dependencies in a data sequence. Secondly, Transformers can parallelly process all elements in a data sequence during training. Finally, a Transformer does not have the vanishing gradient issue. Realizing the immense possibility of Transformers, this paper proposes inTersection-Transformer (inTformer), a time-embedded attention-based Transformer model that can effectively predict intersection crash likelihood in real-time. The proposed model was evaluated using connected vehicle data extracted from INRIX and Center for Advanced Transportation Technology (CATT) Lab's Signal Analytics Platform. The data was parallelly formatted and stacked at different timesteps to develop nine inTformer models. The best inTformer model achieved a sensitivity of 73%. This model was also compared to earlier studies on crash likelihood prediction at intersections and with several established deep learning models trained on the same connected vehicle dataset. In every scenario, this inTformer outperformed the benchmark models confirming the viability of the proposed inTformer architecture.