  Low-energy magnetic excitations in the spin-1/2 chain compound
(C$_6$H$_9$N$_2$)CuCl$_3$ [known as (6MAP)CuCl$_3$] are probed by means of
tunable-frequency electron spin resonance. Two modes with asymmetric (with
respect to the $h\nu=g\mu_B B$ line) frequency-field dependences are resolved,
illuminating the striking incompatibility with a simple uniform $S=\frac{1}{2}$
Heisenberg chain model. The unusual ESR spectrum is explained in terms of the
recently developed theory for spin-1/2 chains, suggesting the important role of
next-nearest-neighbor interactions in this compound. Our conclusion is
supported by model calculations for the magnetic susceptibility of
(6MAP)CuCl$_3$, revealing a good qualitative agreement with experiment.
