* Chilly weather seen continuing through April * Stock-building season off to a slow start * Nuclear plant outages above year ago and five-year average By Joe Silha NEW YORK, April 19 (Reuters) - U.S. natural gas futures ended higher on Friday for the fourth straight session, backed by chilly weather forecasts for the next 10 days that should underpin heating demand despite early selling on profit taking ahead of the weekend. Gas inventories started the heating season at record highs, but cold late-winter weather, a chilly spring and above-average nuclear plant outages have put a huge dent in inventories and prompted higher price estimates for this year. "People are looking at storage (in deficit), and the weather forecasts look fairly supportive. The supply-demand balance is not loose enough yet, so there's still opportunity for more upside," said Steve Mosley at The SMC Report in Arkansas. Front-month gas futures on the New York Mercantile Exchange ended up 0.7 cent at $4.408 per million British thermal units after stalling at $4.42, just shy of Thursday's 21-month high of $4.429. The front contract, which gained 6.6 percent in the last four sessions, ended the week up 4.4 percent, the ninth straight weekly rise. Front-month prices have mostly been in an uptrend since mid-February, gaining some 40 percent in the last nine weeks. But with weather bound to turn milder soon and slow overall demand, concerns are growing that the market may be ripe for a pullback. The record growth in futures open interest that has accompanied recent price gains means there are a lot of new longs in the market who may rush to take profits as moderating spring temperatures finally slow space heating needs. Traders also note that gas prices are at levels that could dampen demand by prompting more utilities to switch back to coal for power generation. High prices may also tempt producers to turn on more wells, increasing supply. Forecaster MDA Weather Services said cool weather should continue in the Plains, Midwest and South for the next 10 days. It said the East Coast was expected to shift to warmer weather later this month and in early May. INJECTION SEASON OFF TO SLOW START A U.S. Energy Information Administration report on Thursday showed total domestic gas inventories rose last week by 31 billion cubic feet to 1.704 trillion cubic feet. Most traders viewed the build as supportive for prices, noting it came in below the Reuters poll estimate of 34 bcf and below the five-year average increase for that week of 39 bcf. The season's first injection, which came about three weeks later than usual, widened the storage deficit relative to the five-year average by 8 bcf, leaving stocks at 74 bcf, or 4 percent, below that benchmark. Chilly weather this month is expected to continue to slow inventory builds and drive stocks further below the five-year average for the next couple of weeks. Early injection estimates for next week's report range from 24 to 48 bcf, versus a 43-bcf build during the same week last year and a five-year average rise for that week of 50 bcf. Injections during the April-through-October stock-building season on average total about 2 tcf, meaning stocks could head into next winter with about 3.7 tcf in the ground, well above what would be needed to meet even the coldest winter demand, but nearly 6 percent below last year's record peak of 3.929 tcf. WHEN WILL OUTPUT SLOW? Baker Hughes data on Friday showed the gas-directed rig count rose this week by two to 379. Two straight weekly gains have stirred expectations that higher gas prices may be tempting producers to bring on more supply. The gas rig count posted a 14-year low of 375 two weeks ago. Drilling for natural gas has mostly been in decline for the past 18 months. The count is down about 60 percent since peaking in 2011 at 936, but so far production has not slowed much from the record high hit last year.