If you eat only chicken and eggs will you lose weight?

A typical chicken breast contains 200 calories. Six of those is 1200 calories, well below the recommended daily limits for both men and women. Taking the RDA for women of 2000 (it will vary around this number), this is a 2000 - 1200 = 800 calorie deficit. 800 calories equates to approximately (and theoretically) 100g of fat lost per day. However, everyone's metabolisms are a little different so there will be a great deal of variation.

But over a long period of time, you will definitely lose lots of weight, because you'll either be dead or in a coma. Eating nothing but chicken breast, or nothing but meat in general, lacks various essential elements of a diet, including various fatty acids (which you need in every cell and can't make from scratch), vitamins and minerals (particularly important as cofactors in enzymes, so good luck surviving without those). Not to mention the extreme difficulty you'd have passing stool on the toilet.

And think of the poor chickens...