It is a common fungal problem of the alliums that affects garlic and leeks more often than chives and onions. With garlic it reputedly saps the strength of the plant causing smaller bulbs. I wouldn't suggest pulling and burning as usually it isn't that bad but don't compost the leaves.
My approach is to cut and burn any badly affected leaves and to give it a dose of Maxicrop.
Here is a thread from last year where Protea made a couple of suggestions including believe it or not, garlic spray.
Rusty Garlic