The request module allows you to pass request headers into the options, so you can do this:
var request = require('request');
var options = {
uri: 'https://api.4chan.org/boards.json',
json: true,
headers: {'If-Modified-Since': 'Sun, 06 Oct 2013 01:16:45 GMT'}
};
request(options, function (error, res, data) {
// other processing
});