Customer service chatbots are increasingly expected to serve not merely as reactive support tools for users, but as strategic interfaces for harvesting high-value information and business intelligence. In response, we make three main contributions. 1) We introduce and define a novel task of Proactive Information Probing, which optimizes when to probe users for pre-specified target information while minimizing conversation turns and user friction. 2) We propose PROCHATIP, a proactive chatbot framework featuring a specialized conversation strategy module trained to master the delicate timing of probes. 3) Experiments demonstrate that PROCHATIP significantly outperforms baselines, exhibiting superior capability in both information probing and service quality. We believe that our work effectively redefines the commercial utility of chatbots, positioning them as scalable, cost-effective engines for proactive business intelligence. Our code is available at https://github.com/SCUNLP/PROCHATIP.