Hi HMB
Right the chain should not move that much so yes it sounds like it needs adjusting.
Now as yours is a Honda you should have the service book with it and this tells you the movement that you should have.
Chain tension is generally determined by the distance between the front and rear sprockets, and many bikes have index marks to help with alignment.
Bikes have differing chain adjustment mechanisms, and in general, the rear axle and wheel move forward or backward in order to set chain tension. Single-sided swingarms usually have an eccentric cam which sets the position of the rear axle; other more traditional designs feature hexagonal-headed inner nuts to move the axle, and an outer one to lock and unlock it.
When chain tension is properly set, it should be able to move up and down between approximately .75 and 1 inch at its loosest point.
I hope this helps......
Iggy
