Chunks of cells after trypsinization
Gibco has an anti-clumping agent verified for CHO cells, as does Lonza, but I like Gibco reagents more. Cells tend to clump for a number of reasons, including extracellular DNA from lysed cells and the presence of Ca and Mg ions (important ions for cell adhesion and aggregation). 

You could try these:

1) Wash and resuspend in balanced salt solution without magnesium or calcium. Like Hank's balanced salt solution.

or

2) Treat with DNase I. I think you could go as low as 1 IU/mL for 30min-1hr to bust up a fair amount of DNA clumping. You can do this in a basal medium (like RPMI, DMEM, etc.), or the balanced salt solution. Your medium can contain serum only if the serum has been heat-inactivated as proteases in the serum with inactivate your DNase. Incubate with DNase under gentle agitation at 37°C (I always had a tube rotator in an incubator for this purpose, just put your cells in a 50mL conical and set them to agitate for 1hr. You could also use a heated shaker unit). If you don't have this setup, you can agitate at room temp, but for a little longer perhaps.

and maybe

3) Once of the other obvious choices is to avoid passaging your clumping cells and collect the rest. You can do this by putting all your cells into a flask incl. the clumps, agitate for a moment, and let it sit so that the chunks quickly fall to the bottom, and collect everything but the stuff that fell to the bottom.