Cannot implicitly convert type 'bool?' to 'bool' Checkbox MVC

Error is self explainary. Your x.Chosen is bool? type (Nullable<bool>).

It mean you should first check it on null. like this for example:

[HttpPost]
public string Index(IEnumerable<City> cities) 
{ 
    if (cities.Count(x => x.Chosen.HasValue && x.Chosen.Value) == 0)
    {
        return "You did not select any city"; 
    }

    ......
}

It's even better to write like this:

[HttpPost]
public string Index(IEnumerable<City> cities) 
{ 
    if (!cities.Any(x => x.Chosen.HasValue && x.Chosen.Value))
        return "You did not select any city"; 
    ......
}

It occurs because the field Chosen is nullable in your database & it is non nullable in your model. To overcome this

[HttpPost]
public string Index(IEnumerable<City> cities) 
{ 
    if (cities.Count(x => x.Chosen.Value) == 0)
    {
        return "You did not select any city"; 
    }
}

or else change the field Chosen in your model as nullable. For Ex.

public bool? Chosen { get; set; }

then you can simply use

if (cities.Count(x => x.Chosen) == 0)