  We consider the Cauchy problem of nonlinear Schr\"odinger equations (NLS)
with almost periodic functions as initial data. We first prove that, given a
frequency set $\pmb{\omega} =\{\omega_j\}_{j = 1}^\infty$, NLS is local
well-posed in the algebra $\mathcal{A}_{\pmb{\omega}}(\mathbb R)$ of almost
periodic functions with absolutely convergent Fourier series. Then, we prove a
finite time blowup result for NLS with a nonlinearity $|u|^p$, $p \in
2\mathbb{N}$. This elementary argument presents the first instance of finite
time blowup solutions to NLS with generic almost periodic initial data.
