It depends on a few factors, breed and individual chicken. Some lay faithfully every day, some every other, some only a couple a week. It depends on what kind of chicken you get. I have Buff orpingtons that lay every day and Polish girls that lay every day for a few days and then skip a day...so they basically lay 4-5 a week.
If you get any production or dual purpose breeds, then yes, this is typically true.. A hens first year is their prime egg laying, it usually slows a little after that. They may be still very productive, but their first year is prime.
Many breeds will also go "out of season" or stop for the winter.. Some breeds are very good at laying all year, some better for laying in winter, some just lay spring, summer, and fall. It just depends on the breed/strain you get and the nutrition provided.
Usually the more ornamental breeds will not lay as much, there are a few exceptions.