I’ve got some railway sleepers to make raised beds from, but need to be able to cut them square so that they sit right when butted at the corners.

I’ve got a chainsaw, but I’m not sure how easy it’ll be to actually follow a line accurately enough to get a square cut?

Other tools available are first fix hand saw, circular saw (won’t cut deep enough), sliding chop saw (again, not enough capacity) or jigsaw (!)

Any tips?

Not a jig saw.
I’d personally use a circular then flip timber.

A decent hand saw?

They are not the evil proper railway sleepers are they that will fill your veggies full of toxic chemicals ?

I guess if there are a few I’d use handsaw, if there are lots I’d set it all up so I could cut half way through a batch of them with circular saw, flip them over and then cut the remaining half.

circular saw, then flip them. its what I did and they look good enough for a veg bed.

Are they ‘proper’ sleepers, as in full of tar?
Wouldn’t want to put any nice tools near that but as above, use a circ saw with maybe a cheap blade fitted.
Make yourself a fence to run the saw along to get the cuts meeting.

They’re not used sleepers, they are new ones but tanalised.

Not softwood. I’ll give it a go with circular saw and hope for the best.

Circular saw and either make a right angle guide like above or get a nice big chunk roofing square like this and clamp it on as a cutting guide.

Cut both sides then finish he bit in between with a handsaw if you need to

They’re not used sleepers, they are new ones but tanalised.

fair enough, if you’re sure
We had several old ones in our garden when we moved in – wept tarry shite whenever the temperature got above about 20 degrees

I did as per Kayak23’s post. Nice and square. I also used new sleepers and the although the blade was not too bad – I replaced it after.