  Semi-infinite quantum spin chains display spin autocorrelations near the
boundary with power-law exponents that are given by boundary conformal field
theories. We show that NMR measurements on spinless impurities that break a
quantum spin chain lead to a spin-lattice relaxation rate 1/T_1^edge that has a
temperature dependence which is a direct probe of the anomalous boundary
exponents. For the antiferromagnetic S=1/2 spin chain, we show that 1/T_1^edge
behaves as T (log T)^2 instead of (log T)^1/2 for a bulk measurement. We show
that, in the case of a one-dimensional conductor described by a Luttinger
liquid, a similar measurement leads to a relaxation rate 1/T_1^{edge} behaving
as T, independent of the anomalous exponent K_rho.

Strongly Correlated Electrons