Chain of length $2^{aleph_0}$in $ (P(mathbb{N}),subseteq)$

How can I find a chain of length $2^{aleph_0}$ in $ (P(mathbb{N}), subseteq )$.

The only chain I have in mind is

$${{0 },{0,1 },{0,1,2 },{ 0,1,2,3},…,{mathbb{N} } }$$

But the chain is of length $aleph_0$, right?