For each given $n\ge 2$, we construct a family of entire solutions $u\_\varepsilon (z,t)$, $\varepsilon > 0$, with helical symmetry to the three-dimensional complex-valued Ginzburg–Landau equation $$ \Delta u+(1-|{u}|^2)u=0, \quad (z,t) \in \mathbb{R}^2\times \mathbb{R} \simeq \mathbb{R}^3. $$ These solutions are $2\pi/\varepsilon$-periodic in $t$ and have $n$ helix-vortex curves, with asymptotic behavior, as $\varepsilon\to 0$, $$ u\_\varepsilon (z,t) \approx \mathop{\smash\[t]{\prod\_{j=1}^n}\vphantom{\prod}} W\bigl(z- \varepsilon^{-1} f\_j(\varepsilon t)\bigr), $$ where $W(z) =w(r) e^{i\theta}$, $z= re^{i\theta}$, is the standard degree $+1$ vortex solution of the planar Ginzburg–Landau equation $\Delta W+(1-|{W}|^2)W=0$ in $\mathbb{R}^2$ and $$ f\_j(t) = \frac{\sqrt{n-1} e^{it}e^{2 i (j-1)\pi/ n}}{\sqrt{|{\log\varepsilon}|}}, \quad j=1,\ldots, n. $$ Existence of these solutions was previously conjectured by del Pino and Kowalczyk (2008), $\mathbf{f}(t) = (f\_1(t),\ldots, f\_n(t))$ being a rotating equilibrium point for the renormalized energy of vortex filaments derived there, $$ \mathcal{W}\varepsilon (\mathbf{f}) := \pi \int\_0^{2\pi} \Biggl( \frac{|{\log\varepsilon}|} 2 \sum{k=1}^n |{f'k(t)}|^2 - \sum{j\neq k}\log |{f\_j(t)-f\_k(t)}| \Biggr) \operatorname{d}t, $$ corresponding to that of a planar logarithmic $n$-body problem. The modulus of these solutions converges to $1$ as $|{z}|$ goes to infinity uniformly in $(t)$, and the solutions have nontrivial dependence on $t$, thus negatively answering the Ginzburg–Landau analogue of the Gibbons conjecture for the Allen–Cahn equation, a question originally formulated by H. Brezis.