Usage of 3DES for single block I have a device, HASP, which has functionality to encrypt 8 byte data using 3DES in ECB mode, with three different keys, I am interested how secure is this?
I know it might not be most secure, but how much? Attacker may query HASP to encrypt something, and try to bruteforce keys from this?

Idea is I thought if I need CBC in my application, I will query the HASP as many times as needed and perform chaining of blocks on PC side.

Or is it better to tell HASP producers to implement encryption of single block however in CBC mode?
If double key DES is used then it is not very secure (63-80 bit security). If tree separate DES keys are used then you'd still have about 112 bits of security. 

That's still not that much, but it would probably not be commercially viable to retrieve the keys of a sentinel using brute force as hacking the application itself is probably a lot more cost effective.

How secure the mode of operation is depends strongly on how the device is used. I'd strongly advice against using the device for anything other than (software protection and) licensing.

These kind of devices often use deprecated encryption that are just barely able to perform the task they've been designed for. When you are encrypting multiple blocks you may already go outside this framework.

That said, in principle the block cipher protects the key whatever mode is used. You'd still not be able to retrieve the key whichever mode you are using - outside brute force and attacking other locations that contain the key or key derivation information of course.