Let $k$ be a field and $R$ be the exterior ring over $k^d $, that is, $k$-algebra generated by elements $$x_1,\ldots,x_d,$$ where $$\ x_ix_j= - x_jx_i?$$
Is $R$ Artinian?
To expand Pete's ḧint:
The key observation is that your $R$ is a finite dimensional $k$-vector space, and each of its left ideals is a vector subspace.
Now consider a decreasing chain of left ideals in $R$... It is in particular a decreasing chain of subspaces in a finite dimensional vector space: can it not stop?
Actually, I am not sure the question is true as stated if $1 = -1$ in $k$!
If $2$ is invertible, then you get $x_i^2=0$ for all $i$. As suggested in the comments and Mariano's answer, the key point is $R$ has finite dimension as a $k$-vector space. Since the monomials span $R$, you want a lot of them to vanish. For example:
$$x_1x_2x_1 = -x_1x_1x_2= -x_1^2x_2 = 0$$