Yes, it is possible to have both chemotherapy and radiotherapy at the same time, and in fact this is quite common. One of the treatments will often be called an "adjuvant" treatment, meaning that is intended to back up the effects of the main treatment.
Whether or not they are given concurrently depends on the specific case. Sometimes you will have a full course of one treatment, then a full course of the other. In other cases they are both done together. You won't have them at exactly the same time, but you might have them on the same day.
Having chemotherapy and radiotherapy at the same time can be pretty intense for the patient, which is why sometimes you are given time to recover from one before starting the other. However, in some cases, it is better to do it all at once to improve the outcome. The doctor will work out which option is the best for your specific case.
I once worked in a hospital where chemotherapy and radiotherapy were given in different buildings. If the chemotherapy team ran late, it sometimes resulted in delays for us in radiotherapy if a patient was having both treatments on the same day.