Most CNN models for chest x-ray diagnosis are computationally intensive both during training and testing. The computational burden may be an inhibiting factor towards the applicability of such models, especially in resource-constrained environments. We propose a computationally lightweight CNN architecture for identifying chest x-ray images with abnormalities. Because of its computational efficiency, our model may be useful even in resource-constrained environments. The proposed parameter-reduced network (PRNet) introduces a channel attention mechanism to achieve superior performance despite parameter reduction using depthwise convolution and squeeze and expand methods. Thus, PRNet helps to reduce model parameters and computational costs without compromising performance. The average AUC obtained using PRNet is as high as 95.66%. Rigorous experiments on publicly available chest x-ray datasets show the utility of the proposed model. Our model has approximately 0.065 million parameters and a size of less than 1 MB. This makes our model useful even with low-end desktop computers or smartphones.