Two squares are chosen at random on a chessboard (see figure). The probability that they have a side in common is:

A chessboard has

$$8\times8=64$$

squares.

Two squares are chosen at random.

Total number of ways:

$$\binom{64}{2}=\frac{64\cdot63}{2}=2016$$

Now count pairs having a common side.

Horizontal adjacent pairs:

Each row has

$$7$$

adjacent pairs.

Since there are

$$8$$

rows,

$$8\times7=56$$

pairs.

Vertical adjacent pairs:

Similarly,

$$8\times7=56$$

pairs.

Hence total favorable pairs:

$$56+56=112$$

Therefore, required probability is

$$\frac{112}{2016}$$

$$=\frac1{18}$$

Hence, the required probability is

$$\boxed{\frac1{18}}$$