As I understand, Fido generally does not price match plans. However, there have been occasions where they have offered special promotional plans in response to promotional plans offered by other providers.
That said, I am doubtful that they would price match a plan from Chatr. I understand they are both subsidiaries of Rogers, but Chatr and Fido offer different services. For example, Chatr does not offer LTE service. In addition, calling and texting with Chatr's plans depend on your location relative to their zones. On the other hand, Fido's current in-market plans all include Canada-wide calling and texting.
Price matching would be same for same (or at least similar) services. It does not make sense to match the price of a plan offering lesser service.
Hope this helps