We have had problems with non indigenous species becoming established in the wild here in the UK. This has caused problems for our native wildlife. Three I can think of are: American Grey Squirrels, Mink and surprisingly Wallabies. With the American Grey squirrels which were released in the 1800's, there is hot debate whether they are the main cause of the decline of our native red squirrel. I think it was Lord Brockenhurst who first imported grey squirrels to add to his estate. Our government class the grey squirrel as vermin. With many people having been surprised when taking an injured grey squirrel to vet, only to have it euthanised without their consent. Mink were released from fur farms by animal rights activist, but mink are partly to blame for the rarity of our water voles.
There has been at least one case where there has been a mass escape of chipmunks (over 40) and the relevant ministry had to be informed. They will either try to capture or kill escaped chipmunks, for fear of them becoming established. In truth there are now wild chipmunks in the UK, all of which have escaped from captivity.
The only species of chipmunks we are likely to have as a pet in the UK is the Eastern European also known as the Siberian chipmunk. But in the USA you have many more species which are native, and you are not alone in having one as a pet in the US. Our chipmunks were first imported to be used in animal vivisection experiments over thirty years ago. Chipmunks are still imported to the UK but I think this is now to keep up with the increasing demand for pet chipmunks. I don't believe wild chipmunks in the UK are out there in enough numbers to become established but the mostly likely reason our Government don't want them established is a threat to bird life. It's reported that chipmunks like most squirrels like to raid birds nests for eggs.
You may have heard the myth the we are a nation of animal lovers here in the UK, sadly I believe we are no better or worse than any other country. Our Government would rather cull any species it fears could be an economic threat, rather than research things properly.