Since this hat is knit in the round, you'll always be reading the chart from right to left. Place a marker on the needle for the beginning of the round. Using a different color, you could also place markers every 2 repeats or so to keep track of your stitches and make sure you don't forget a yo or a k2together. These markers can be a simple as a loop of scrap yarn.
If it were knit flat, you would read row 1 (and all odd rows) right to left and row 2 (and all even rows) left to right.