Let $q\in\mathbb N$, let $a\in\mathbb Z$ satisfy $\gcd(a,q)=1$, and let $x\in\mathbb R$ satisfy $x>q+1$. Let $\varphi:\mathbb N\to\mathbb N$ denote Euler's totient function. Let $\log:(0,\infty)\to\mathbb R$ denote the natural logarithm. Define $\pi(x;q,a)$ to be the number of primes $p$ such that $p\le x$ and $p\equiv a\pmod q$. Then
\begin{align*}
\pi(x;q,a)\le \frac{2x}{\varphi(q)\log(x/q)}.
\end{align*}