What procedures have you tried so far? An appropriate non nucleophilic base to deprotonate the TEG without reacting with the chloroacetic acid is a start, maybe KOtBu and reaction solvent of THF if the TEG is soluble in it. You could cool a mixture of TEG in THF and add KOtBU in a THF solution dropwise while stirring. Then I would add the chloracetic acid dropwise. Maybe this will work. Purification will be annoying as there will be a mixture of products. The difficulties are outlined here in this paper

http://onlinelibrary.wiley.com/doi/10.1002/anie.201410309/epdf

I used chloroacetic acid to react with alcoholic OH groups in the presence of K2CO3 as a base and KI as a catalyst for the substitution reaction. The reactions were carried out in DMF at a temperature between 40 and 60 celsius to speed up the reaction.

You can acidify at the end of the reaction to convert the acetate groups to acetic acid substituents.

See the following paper (see my profile):

Removal of heavy metals from wastewater by economical polymeric collectors using dissolved air flotation process

Article in Journal of Water Process Engineering 8:19-27 · August 2015 

To 0.2 mole tetraethyleneglycol add of 0.3 mole of dry crushed potash with vigorous stirring (at to = 30o C) and was dropwise added 0.025 mol of the acid chloride chloroacetic acid during of 1 hour. The temperature was then raised to 60 ° C and stir until the reaction is complete (chromatographic control).