We present a novel multimodal dataset for Cognitive Load Assessment in REaltime (CLARE). The dataset contains physiological and gaze data from 24 participants with self-reported cognitive load scores as ground-truth labels. The dataset consists of four modalities, namely, Electrocardiography (ECG), Electrodermal Activity (EDA), Electroencephalogram (EEG), and Gaze tracking. To map diverse levels of mental load on participants during experiments, each participant completed four nine-minutes sessions on a computer-based operator performance and mental workload task (the MATB-II software) with varying levels of complexity in one minute segments. During the experiment, participants reported their cognitive load every 10 seconds. For the dataset, we also provide benchmark binary classification results with machine learning and deep learning models on two different evaluation schemes, namely, 10-fold and leave-one-subject-out (LOSO) cross-validation. Benchmark results show that for 10-fold evaluation, the convolutional neural network (CNN) based deep learning model achieves the best classification performance with ECG, EDA, and Gaze. In contrast, for LOSO, the best performance is achieved by the deep learning model with ECG, EDA, and EEG.