Let $ \overline B=\{ \overline B_{t},t\in R^{1} \}$ be Brownian motion killed after an independent exponential time with mean $2/λ^{2}$. The process $\overline B$ has potential densities, \[ u(x,y) ={e^{-λ|y-x|}\over λ},\qquad x,y\in R^{ 1}, \] which is also the covariance of an Ornstein--Uhlenbeck process. Let $f$ be an excessive function for $\overline B$. Then, \[ {e^{-λ|y-x|}\over λ}+f(y),\qquad x,y\in R^{ 1}, \] is the kernel of an $α$-permanental process $ X_α=\{ X_α(t), t\in R^{ 1}\}$ for all $α>0$. It is shown that for all $k\ge 1$ and intervals $Δ\subseteq [0,1] $, \[ \limsup_{h\to 0}\sup_{\stackrel{|u-v|\le h }{ u,v\inΔ}} \frac{|X_{k/2} (u)-X_{k/2} (v)|}{ 2 ( |u-v| \log 1/|u-v|)^{1/2}}= \sqrt 2 \sup_{t\inΔ}X_{k/2}^{1/2}(t)\qquad a.s.\] The local modulus of continuity of $X_{k/2}$ for all $k\ge 1$ is also obtained. Local and uniform moduli of continuity are also obtained for chi--square processes which are defined by, \[ Y_{k/2}(t)=\sum_{i=1}^{k}\frac{η^2_{i}(t)}{2},\qquad t\in [0,1], \] where $η=\{η(t);t\in [0,1]\}$ is a mean zero Gaussian process and $\{η_{i};i=1,\ldots, k\}$ are independent copies of $η.$