Aiming at the complex nonlinear relationship between temperature rise and spindle thermal error caused by multiple heat sources of numerical control (NC) machine tool, a spindle thermal error prediction model (hereinafter referred to as thermal error model) based on chicken swarm optimization (CSO) algorithm and support vector machine (SVM) was proposed. Taking the spindle unit of a precision NC machine tool as the research object, the axial thermal deformation under idle state was measured by five-point measurement method, and the temperatures of four key temperature measuring points of the machine tool were collected using thermocouple sensor. Based on SVM theory, 75% data samples were randomly selected for training, and then the spindle thermal error model was constructed. Among them, CSO algorithm was used to optimize the penalty parameter c and kernel parameter g of SVM model to improve the prediction ability and robustness of the thermal error model. The remaining 25% of the samples were used as the test data set to verify the thermal error model.The spindle thermal error under different working conditions was predicted using CSO-SVM model, and the predicted results were compared with the measured results.The results showed that when the spindle rotate speed was 3 000 r/min, the average prediction accuracy of CSO-SVM model was as high as 97.32%, which was 6.53% and 4.68% higher than that of multiple linear regression model and SVM model based on particle swarm optimization, respectively; when the spindle rotate speed was 2 000 and 4 000 r/min, the average prediction accuracy of CSO-SVM model was 92.53% and 91.82% respectively, indicating that the model had high prediction ability and good robustness. CSO-SVM model has strong practicability and engineering application value.