It is not permitted to connect the ground to the neutral wire.
Putting a GFCI receptacle as the first device in the circuit is a good idea as it will provide for Ground Fault protection there and on downstream devices connected back to the Load terminals of the GFCI. Not as good as also having a ground wire, but better than no protection. The receptacles must then be labeled as 'Ungrounded'

Specifically the code requires the words "NO EQUIPMENT GROUND." Usually the GFCI comes with some appropriate stickers for you to use.

You may want to find another electrician though... I can't imagine any qualified electrician suggesting that the ground be connected to the neutral.

Here's why that's a hugely bad idea: in the event that the neutral wire would break or have a bad connection, all of the metal surfaces of an appliance, for example, would become energized. Depending on where the break happened, it could potentially energize all of the "grounded" surfaces including faceplates, metal surfaces, etc on anything plugged into the entire circuit.

This type of grounding is known as a "bootleg ground". It's done to fool home inspectors. No legitimate electrician would suggest doing it - even with a GFCI (which can fail).

Thank you all

It's not even a "bootleg" ground. Grounding to the neutral is unsafe and only permitted in certain cases (grandfathered stove and dryer situations), certainly NOT in this case. It's UNSAFE for a number of reasons.

A bootleg ground is using a grounding conductor of another circuit. This is less of an issue but still possibly problematic but also possibly permitted by the code.

ronnatalie,

I know different people have different informal terminology for these things... but if you google "bootleg ground" you will see that connecting the ground to the neutral is a common definition.

At any rate, it's not something that should be done. Neither would the electrician accomplish anything by connecting the ground to the metal box unless the metal box is grounded - for example through BX or armored cable.

BX is not recognized as an adequate ground either.

ronnatalie,

I guess I wasn't very clear. My point was simply grounding to a metal box that had no ground path wouldn't accomplish anything - and having someone suggest that would cause me to question the competency of the electrician.

I wasn't commenting on if grounding to a box with an old but intact BX ground was an adequate or code approve retrofit (because I didn't know for sure). But thanks for clearing that up.