In this paper, we present an approach to monitor the Italian public opinion from tweets analysis, with reference to the vaccination topic. This topic has recently become controversial, due to the disinformation about the alleged connection between autism and vaccines. Further, the Italian Ministry of Health has noticed a drop in vaccination rates, enhancing the risk of reemergence of eradicated diseases. Thus, a system to monitor the negative public opinion about vaccines could become very important for decision making. The proposed approach i) fetches vaccine-related tweets, ii) applies a text elaboration on the tweets, and iii) performs a binary classification aimed at discriminating negative opinions tweets (i.e., not in favor of vaccination) from the rest of tweets. By employing the Simple Logistic classifier, we achieved a 75.5% average accuracy. Finally, we monitor the trend over time of public opinion about vaccination decision making in a free, real-time and quick fashion.