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We prove a lower bound for the free energy (per unit volume) of thetwo-dimensional Bose gas in the thermodynamic limit. We show that the freeenergy at density $\rho$ and inverse temperature $\beta$ differs from the oneof the non-interacting system by the correction term $4 \pi \rho^2 |\ln a^2\rho|^{-1} (2 - [1 - \beta_{\mathrm{c}}/\beta]_+^2)$. Here $a$ is thescattering length of the interaction potential, $[\cdot]_+ = \max\{ 0, \cdot\}$ and $\beta_{\mathrm{c}}$ is the inverse Berezinskii--Kosterlitz--Thoulesscritical temperature for superfluidity. The result is valid in the dilute limit$a^2\rho \ll 1$ and if $\beta \rho \gtrsim 1$.

The free energy of the two-dimensional dilute Bose gas. I. Lower bound