  We present an electron spin resonance (ESR) study of single-crystalline spin
chain-system CuSe$_2$O$_5$ in the frequency range between 9 GHz and 450 GHz. In
a wide temperature range above the N\'{e}el temperature $T_N=17$ K we observe
strong and anisotropic frequency dependence of a resonance linewidth. Although
sizeable interchain interaction $J_{IC}\approx 0.1 J$ ($J$ is the intrachain
interaction) is present in this system, the ESR results agree well with the
Oshikawa-Affleck theory for one-dimensional $S=1/2$ Heisenberg antiferromagnet.
This theory is used to extract the anisotropies present in CuSe$_2$O$_5$. We
find that the symmetric anisotropic exchange $J_c=(0.04 \pm 0.01) \:J$ and the
antisymmetric Dzyaloshinskii-Moriya (DM) interaction $D=(0.05\pm 0.01)\:J$ are
very similar in size in this system. Staggered-field susceptibility induced by
the presence of the DM interaction is witnessed in the macroscopic
susceptibility anisotropy.
