  We examine the inner mass distribution of the relaxed galaxy cluster Abell
383 in deep 16-band HST/ACS+WFC3 imaging taken as part of the CLASH multi-cycle
treasury program. Our program is designed to study the dark matter distribution
in 25 massive clusters, and balances depth with a wide wavelength coverage to
better identify lensed systems and generate precise photometric redshifts. This
information together with the predictive strength of our strong-lensing
analysis method identifies 13 new multiply-lensed images and candidates, so
that a total of 27 multiple-images of 9 systems are used to tightly constrain
the inner mass profile, $d\log \Sigma/d\log r\simeq -0.6\pm 0.1$ (r<160 kpc).
We find consistency with the standard distance-redshift relation for the full
range spanned by the lensed images, 1.01<z<6.03, with the higher redshift
sources deflected through larger angles as expected. The inner mass profile
derived here is consistent with the results of our independent weak-lensing
analysis of wide-field Subaru images, with good agreement in the region of
overlap. The overall mass profile is well fitted by an NFW profile with
M_{vir}=(5.37^{+0.70}_{-0.63}\pm 0.26) x 10^{14}M_{\odot}/h and a relatively
high concentration, c_{vir}=8.77^{+0.44}_{-0.42}\pm 0.23, which lies above the
standard c-M relation similar to other well-studied clusters. The critical
radius of Abell 383 is modest by the standards of other lensing clusters,
r_{E}\simeq16\pm2\arcsec (for z_s=2.55), so the relatively large number of
lensed images uncovered here with precise photometric redshifts validates our
imaging strategy for the CLASH survey. In total we aim to provide similarly
high-quality lensing data for 25 clusters, 20 of which are X-ray selected
relaxed clusters, enabling a precise determination of the representative mass
profile free from lensing bias. (ABRIDGED)
