Using molecular line data from the Millimetre Astronomy Legacy Team 90 GHz Survey (MALT90), we have searched the optically thick hcop, line for the blue asymmetry spectroscopic signature of infall motion in a large sample of high-mass, dense molecular clumps observed to be at different evolutionary stages of star cluster formation according to their mid-infrared appearance. To quantify the degree of the line asymmetry, we measure the asymmetry parameter $A = {{I_{blue}-I_{red}}over{I_{blue}+I_{red}}}$, the fraction of the integrated intensity that lies to the blueshifted side of the systemic velocity determined from the optically thin tracer thp. For a sample of 1,093 sources, both the mean and median of $A$ are positive ($A = 0.083pm0.010$ and $0.065pm0.009$, respectively) with high statistical significance, and a majority of sources (a fraction of $0.607 pm 0.015$ of the sample) show positive values of A, indicating a preponderance of blue-asymmetric profiles over red-asymmetric profiles. Two other measures, the local slope of the line at the systemic velocity and the $delta v$ parameter of citet{Mardones1997}, also show an overall blue asymmetry for the sample, but with smaller statistical significance. This blue asymmetry indicates that these high-mass clumps are predominantly undergoing gravitational collapse. The blue asymmetry is larger ($A sim 0.12$) for the earliest evolutionary stages (quiescent, protostellar and compact H II region) than for the later H II region ($A sim 0.06$) and PDR ($A sim 0$) classifications.
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