An early board game which players moved their counters around the squares?

That description fits a lot of early board games, but some of the most famous and early examples include:

* Senet: This ancient Egyptian game dates back to 3500 BCE. Players moved counters around a board with 30 squares, with the goal being to reach the opposite end of the board before their opponent.

* Royal Game of Ur: This game, from ancient Mesopotamia (circa 2600 BCE), used a board with 20 squares. Players moved counters around the board, aiming to be the first to reach the end.

* Pachisi: This Indian game, which dates back centuries, is played on a board with 64 squares. Players move counters around the board, attempting to be the first to get all of their pieces home.

It's impossible to definitively say which of these is the earliest board game with counters, but these are all excellent examples of early games with similar mechanics.