  We present a non-parametric method to measure inhomogeneities in the
intracluster medium (ICM) from X-ray observations of galaxy clusters. Analysing
mock Chandra X-ray observations of simulated clusters, we show that our new
method enables the accurate recovery of the 3D gas density and gas clumping
factor profiles out to large radii of galaxy clusters. We then apply this
method to Chandra X-ray observations of Abell 1835 and present the first
determination of the gas clumping factor from the X-ray cluster data. We find
that the gas clumping factor in Abell 1835 increases with radius and reaches
~2-3 at r=R_{200}. This is in good agreement with the predictions of
hydrodynamical simulations, but it is significantly below the values inferred
from recent Suzaku observations. We further show that the radially increasing
gas clumping factor causes flattening of the derived entropy profile of the ICM
and affects physical interpretation of the cluster gas structure, especially at
the large cluster-centric radii. Our new technique should be useful for
improving our understanding of the cluster structure and to advance the use of
galaxy clusters as cosmological probes, by helping to exploit rich data sets
provided by Chandra and XMM-Newton X-ray space telescopes.
