We present a clustering analysis of Luminous Red Galaxies in SDSS Stripe 82. We study the angular 2-point correlation function, of 130,000 LRG candidates via colour-cut selections in izK with the K band coverage coming from UKIDSS LAS. We have used the cross-correlation technique of Newman (2008) to establish the LRG redshift distribution. Cross-correlating with SDSS QSOs, MegaZ-LRGs and DEEP2 galaxies implies an average LRG redshift of z~1 with space density, n_g~3.2 +/-0.16 x10^-4 h^3 Mpc^-3. For theta<10', w(theta) significantly deviates from a single power-law. A double power-law with a break at r_b~2.4 h^-1 Mpc fits the data better, with best-fit scale length, r_0,1=7.63+/-0.27 h^-1Mpc and slope gamma_1=2.01 +/-0.02 at small scales and r_0,2=9.92 +/-0.40 h^-1 Mpc and gamma_2=1.64 +/-0.04 at large scales. Due to the flat slope at large scales, we find that a standard LambdaCDM linear model is accepted only at 2-3sigma, with the best-fit bias factor, b=2.74+/-0.07. We also fitted HOD models and estimate an effective halo mass of M_eff=3.3 +/-0.6x10^13 h^-1 M_sun. But at large scales, the current HOD models did not help explain the power excess in the clustering signal. We then compare the w(theta) results to those of Sawangwit et al. (2011) from 3 samples of LRGs at lower redshifts to measure clustering evolution. We find that a long-lived model may be a poorer fit than at lower redshifts, although this assumes that the Stripe 82 LRGs are luminosity-matched to the AAOmega LRGs. We find stronger evidence for evolution in the form of the z~1 LRG correlation function, with the above flat 2-halo slope maintaining to r>50 h^-1 Mpc. Applying the cross-correlation test of Ross et al. (2011), we find little evidence that the result is due to systematics. Otherwise it may provide evidence for primordial non-Gaussianity in the matter distribution, with f^local_NL=90+/-30.[Abridged]

20 pages, 25 figures, accepted for publication in MNRAS, more tests for systematics errors checked (Fig. 22-23), conclusions remained the same