Does this distribution make any sense?

Does this distribution make any sense?

I met this distribution $u$ which acts like $$ \langle u, \phi \rangle =
\int _{\mathbb{R}} \frac{\phi (t)}{t^n}\,dt , \qquad \phi \in C_0^\infty
(\mathbb{R}) $$ where $n\ge 2$ is an integer. Is this well-defined the way
it stands? Or does it have to be written as $\lim_{\varepsilon \to 0}
1/(t\pm i\varepsilon )^n$?
Otherwise, could I say something about it in terms of $\phi (0)$?