Semi-infinite quantum spin chains display spin autocorrelations near the bo
undary with power-law exponents that an given by boundary conformal field t
heories. 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 bound
ary exponents. For the antiferromagnetic S = 1/2 spin chain, we show that 1
/T-1(edge) proportional to T log(2)T instead of log(1/2)T for a bulk measur
ement. We show that, for a one-dimensional conductor described by a Lutting
er liquid, a similar measurement leads to a rate 1/T-1(edge) proportional t
o T, independent of the exponent K-rho.